How To Solve For The Angle - Viral Math Challenge

This is a pretty tricky problem. Can you solve for the angle? Watch the video for the solution. I thank Barry, and I thank Akshay Dhivare from India for suggesting the problem via email.
Sources
gogeometry.blogspot.com/2008/...
• Problem 010
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[@orenaharoni8763]

what i learn in class: 1+2 homework: 7+5 test:

[@anuradhamd263]

😂

[@michaelroditis1952]

Loved it 😂😂

[@sevast7853]

simply perfect

[@carlosthomas4565]

😂

[@fratbas3939]

😂😂😂

[@tschantz]

I spent hours on this because it looks so simple and I refused to give up. It looks like we have all the information we need. I kept thinking there has to be a right triangle in here somewhere that Pythagorus can help me with. I drew circles, right triangles, extended the lines outside the big triangle, sliced the isosceles in half to form two 10° 80° right triangles...Nope. I gave up. Never in my wildest dreams would I have constructed an equilateral and then some weird scalene that happens to be congruent to Mercury's retrograde rising over the perihelion of Andromeda.

[@abcd-lb1ty]

idk ive just started learning pythagoram so im not that good. but i solved this problem im like 20 seconds. if you see the 20 degree point, you can draw a line to create another 20 20 140 triangle. the other side of 20 degree line is 160. (180-20). Then the other angles in the 160 angle triangle is 10 10. so 140+10= 150 180-150=30

[@stewbaka4279]

@@abcd-lb1ty sorry but could you elaborate im very confused...

[@kartikpatyal]

​@@abcd-lb1ty ohkay but how do uk that in 160° triangle the other two angles will be equal/that triangle is isosceles?

[@rayaanansari4834]

@@kartikpatyal the triangle must be perfectly symmetric. Draw the perpendicular lines from the point with the different angle and use the Pythagorean theorem maybe

[@abeonthehill166]

I knew it could be solved …….so i did what i always do when life gets tough. I cheated by watching the solution then re-ran the video solution to see how the correct answer was calculated ! My method is actually very effective !

[@shototodoroki2034]

Problem: Alright, solve for this angle. Solution: Create multiple triangles until you get what you want

[@ashthepokemonmaster2375]

Shoto Todoroki LoL ikr

[@detectiveexpressking4078]

There's an easier solution: Since you know that the whole triangle is an isoceles, you also know that when contructing a rectangle, the distance of the rectangle's sides from the sides of the isoceles will be equal. From this, you know that the 80 degree angles on the whole triangle are consecutive on their sides with the exterior angles bounding the 20 degree vertex: -->80+80+20=180 These angles make a right riangle on each side, so you know that:(on the upper side ( the important one) 90=(80+(180-(90+80)) =80+10* 10 is the angle that makes the 80 degree angle into a 90 degree. Since the whole triangle forms an isoceles (with two 80 degree angles), and since the second 80 degree angle is formed with the addition of another triangle (scalene), the important triangle is also a scalene. The addition of this angle with 10 creates 80. That ten is equivalent to the other calculated. 10+?#= 80 ?#=70 70+80+?$=180 ?$=30°

[@panagiotisdeligiannis9610]

Anyone: I feel very confident of my math skills. Presh: Can you solve this problem that was given to newborns in China?

[@michaelroditis1952]

I know!!

[@Seedx]

Lol same

[@3bydacreekside]

I already knew I wasn't gonna solve it...and I didn't xD

[@al9able1]

china??? ha ah ha

[@personpqr6153]

This is indian

[@nicolasortiz4422]

And it's because of problems like this that trigonometry was invented

[@angelmendez-rivera351]

Actually, this already technically counts as trigonometry.

[@zeroanims4113]

How to solve this using trigonometry?

[@ilprincipe8094]

@@zeroanims4113 i dont have a concrete answer, but you basically just describe the 2 equal sides with cosine rules and then solve for x, its quite simple actually

[@mouradleo]

@@ilprincipe8094 explain more

[@ilprincipe8094]

@@mouradleo sorry I actually meant sine rules. Okay, first off you have to label some sides, the both sides which are equal are called "a", the side to the "right" of the 80° angle is b ( so a+b is the length of the "lowest" side, hope you understand) and then we need to label the side in the middle, which cuts the side a+b into "a" and "b", lets call it "c". The triangle has an angle of 180 - 80 - 20 = 80° on the top corner, this angle is getting split by "c" into two (unequal) angles, lets call them "beta" (the angle for the left triangle) and "gamma" (the angle for the right triangle). Okay, so far so good. Now all we gotta do is to describe the side "a" in two different ways. The sine rule is : a / sin (alpha) = b / sin (beta) That means a = (b * sin (alpha)) / sin (beta) Now its important to not get confused by a and alpha and so on, it would be very good to draw a triangle and label the sides a b c and the angles alpha beta gamma so you can always see the relation. Okay whatever. Now we described "a" using the left triangle, and as you might see, we actually dont even now b, alpha or beta. Hm, thats a problem but it can be solved. B can actually be set to any value, because if we know 3 angles and 0 sides there are infinite possibilities, but the sides always have a certain ratio because of the angles, in this case, we dont even have to assume anything, since "b" will just completely cancel out later. Okay. "Alpha" is the angle we are looking for. We can describe it using Alpha = 180 - 80 - Beta Goddamn, we dont now Beta either. But we now that "Beta" + "Gamma" = 80° In this solution, we actually first calculate the value for "beta" and then alpha, so for a we get: a = (b * sin(180-80-Beta))/sin (Beta) Now lets describe a in the right triangle. a / sin (Gamma) = e / sin(20) Eh im a bit short on time, if you want me to keep going just tell me

[@vankrelian]

Things I learned from watching this channel: when in doubt, just try sticking an equilateral triangle or circle somewhere.

[@unknownobserver4675]

vankrelian Perfect

[@arthurg.machado6803]

I went the circle path, didn't work out for me this time.

[@valasfar1557]

vankrelian This is actually very good advice for geometry in competition math. And if they don’t work, try creating a perpendicular instead.

[@appuappuappu7061]

😑for me the solution is wrong, 'cause it didn't even match the simple theorem that, "all interior angles of a triangle always adds up to 180 degree".... Now tell me why the solution is not fitting in it🙃, are these not triangles 😑???

[@laerteb.6302]

6

[@Sam-ps5xs]

I'm a geometry tutor and I spent like 10 mins thinking and finally ended up watching solution...

[@TarunKumar-qs9dj]

U should quit Android mobile so that ur should get inspired by u.

[@aayushpotdar1592]

Noife

[@ubitchesaremysons6897]

Am scared for your students

[@molotovtheholy2292]

@@ubitchesaremysons6897 teachers are not necessarily able to solve everything. This question is insanely hard (geometrically speaking of course) so a majority of people can not solve it is understandable.

[@mohamednasser4182]

It doesn't depend on intelligence i think it depends on learning

[@atulchauhan5565]

Nobody - Indian competition exams- you have to solve this in 20 seconds.

[@riyarishika8920]

u know ... i m a n indian , s nd this * does not * happen

[@NightwingGFX]

@@riyarishika8920 no, it does and I'm not even india

[@agsheuehd]

Lol don't a lot of countries in Asia do that?

[@thecreator4541]

@@riyarishika8920 I am also Indian...we solved this question in class 9...it was exactly the same question

[@tareqalhossain2659]

There are some Question in competitive exam,which are given for ranking and loss ur time...If u r an ordinary student u should skip this and try another one🙂

[@manshisinha7953]

*I kneww it. That **_looked_** like a 30°.*

[@suhaibrashid6083]

Haha Same if it were mcq

[@mfaris259]

everytime after geometry test :

[@suhaibrashid6083]

@@mfaris259 😂😂 Literally the second after the exam is over you get all sorts of ideas😂

[@chanbaekshii4682]

Me to

[@matheuscipriano7]

I said was a 25° haha

[@jsfbr]

This solution demands tons of experience with geometry.

[@jessstuart7495]

There have been a few other MindYourDecisions videos where you drew extra isosceles and equilateral triangles to help you solve for an unknown angle. After getting stuck on this problem, I'll definitely remember this trick.

[@walrusninja3581]

jsfbr as a freshman in high school only one semester in, I new every law. I tried solving this for a few minutes but quickly realized I couldn’t. Other than the use of auxiliary lines which I was not expecting, it requires little experience in geometry

[@BudderB0y2222]

@@walrusninja3581 It's easy once you have the lines, but the challenging part is knowing where to draw them and recognizing relationships, as well as being able to focus on one triangle

[@iannisdezwart]

I actually solved it and I just learned geometry at school

[@stardustreverie6880]

@@iannisdezwart 👏👏👏👏👏👏👏👏

[@selinniesy]

I'm from Turkey, our geometry teacher teaches us this kind of problems as "cut-paste" questions. In well-prepared geometry books we often use this technique.

[@user-ey1hf8mw9q]

our edu system is bad but we learn a lot of hard problems and our university exams(to start a university) has hard questions too. If we rate this question 10 points, Turkey's exam questions will have 5-7 points. Hard ones can get 8-8,5

[@Userf471]

@@user-ey1hf8mw9q this question is for middle class in turkey and this guy talks about easy question like hard

[@user-ey1hf8mw9q]

@@Userf471 YES most of Turkish students can solve this middle class question but I'm talking about exam, you should solve this in 2 minutes, that makes it hard. Have a great day comrade.

[@cikolatalmilkshake4302]

Cut-paste şeysini anlatır mısın🤗

[@selinniesy]

@@cikolatalmilkshake4302 Bizim öğretmenimiz bize bu tip soruları "kes-yapıştır soruları" diye anlatmıştı. Yani bu videoda adamın anlattığı şeyin aynısı. Verilen şekilde bilginin çok olduğu kısmın aynısını, o bilgiyi kullanabileceğin bir yere çiziyosun. Genelde ikizkenar üçgenler falan çıkıyo ordan da soru çıkıyor zaten. Biraz karışık oldu ama umarım anlatabilmişimdir. Yeterli gelmezse birçok üçgenler soru çözümü videosunda bu tekniği bulabilirsin 😊😊

[@annettemeyer1393]

i have only just stumbled on your videos. I left school more than 50 years ago, so my mathematical skills are really rusty, but I am so enjoying the stimulation of working these questions out. I don't get many on my first try. I love your very clear explanations. Thank You.

[@pipertripp]

"did you figure it out?" Hell no. But what a clever solution. That was like a chess match, layer on layer of scaffolding to get at the crux, those last two congruent triangles. Impressive.

[@philiphall4805]

Using a protractor would be the easiest and quickest way by far

[@brad1ey50]

This is like when a grandmaster in chess finds the most insane move that wins them the game

[@yogeshsharma4723]

Who else started with angle 'x' and ended up his equations by canceling out +x and - x and all thats left is 180.

[@TasnimulHasanTahsin]

Mee😆😆

[@wyjer7286]

my first answer was Rihanna...

[@user-dd7kl5cw1p]

Same here.... 😂

[@shreerangvaidya9264]

I used y but yeah.

[@shotto9167]

I just used basic algebra, but the result was equal to 20°.

[@UltraSexyChipotle]

Video: don't use trigonometry Me: no

[@Kishgofu]

i'm curious, how would you use trigonometry to figure this out?

[@grifferkay9253]

I was correct till here 1:31

[@aayushpotdar1592]

I went a little further too (without sticking the frickin triangles everywhere) but got the answer as 20°

[@krish1349]

Lol😂

[@yousiffaris696]

Same

[@phenomenalphysics3548]

wow!!

[@allisonfisher5126]

This looked much easier that it was...

[@portobellomushroom5764]

@@angleturner the difference knowing trigonometry and how to use it makes

[@allisonfisher5126]

@@angleturner r/iamverysmart

[@Riiisuu]

angleturner r/ididntdoitbutimsureiwoildvegotitsometimeintheforseeablefuture

[@tharunmalayil2332]

Oh yeah yeah..

[@sonpham3438]

Oh yeah yeah

[@fatiherensasmaz]

Türkçe alt yazıyı yapandan Allah razı olsun. ❤

[@canertaskn2712]

:)

[@fatiherensasmaz]

@@canertaskn2712 sen mi yaptın? :) Harikasın.

[@heyyitsmeyouknowwhoiam1991]

allah gercek degil

[@canertaskn2712]

@@fatiherensasmaz keşke ben yapsaydım. Ben yapmadım

[@canertaskn2712]

@@heyyitsmeyouknowwhoiam1991 uluslararası bir matematik kanalında birisi alt yazıyı yapana teşekkür ediyor.Ve sen de teşekkür etme şeklini eleştiriyor. Ne kadar cahilce ve orta çağ yaklaşımı

[@fashidox]

Love channels like this, 3Blue1Brown, Mathologer. It's like a fun way to revise and you even forget you're revising. Ways to think outside the box. Awesome.

[@schino]

well... using a protractor is elementary geometry too

[@digiquo8143]

Triangles drawn on tests won't always be to scale, and usually only use approximations for angle measurements specifically so you can't just whip out a protractor.

[@schino]

@@digiquo8143 yeah, i know.

[@theseeker7194]

@@digiquo8143 r/wooosh

[@dakotayupyupyup8377]

Digiquo that’s completely unrealistic though “Solve this impossible triangle” is equivalent to “let’s start using imaginary numbers that literally can’t exist” in math.

[@acswain6720]

You fail if image is hand drawn and NOT UPTO SCALE.

[@kabirmalik1582]

Nice video Presh!!! These are great (especially the geometry ones!) it’s definitely a fun watch for me

[@deepankchauhan8061]

Nice video

[@hydra147147]

One can also consider a regular 18-gon A1...A18 with the center O. Then the triangle in question is exactly the same as A1OA2 and the constructed point (lets call it P) is the intersection of the lines OA2 and A1A8. We can show that by noticing that OP=0.5XA9 where X is the intersection of A5A9 and A1A8 because it is a midline and XA9=2A8A9 because the triangle XA8A9 is the half of an equilateral triangle, so OP=A8A9=A1A2 therefore it is indeed the desired point. Then the rest easy follows from an angle chasing. Also do note that solution in the video constructs the equlateral triangle and it's third vertex is A3 and the solution in the pinned comment by Nestor Abad considers another equilateral triangle and it's third vertex is the intersection of two lines A1A7 and A2A12 so all solutions seem to rely on the underlying structure of an regular 18-gon.

[@ecatuccio]

I'd like to see this.

[@serendipitousillicit734]

Hello, fellow Ricardo and Mortimus fan

[@yourlordandsaviouryeesusbe2998]

@@serendipitousillicit734 lmao

[@spacescopex]

Please try MY SOLUTION: kzbin.info/www/bejne/bqnUpYFppM-Ygq8

[@kyle_liao6225]

This channel's videos accompany me with many enjoyable lunch for days, and to this particular puzzle I also come up with a alternative solution, and no need to use pen and paper, just imagine in mind. 1. Draw a equilateral triangle on the left side so the bottom left corner can divided into 60° and 20°. 2. Rotate and move the 20° triangle on the right side to match up the bottom left corner of the isosceles triangle. 3. Now because the cut away triangle have 3 condition: ONE side equals to the equilateral triangle, ONE side equals to the isosceles triangle, ONE angle equals to 20°, it can flip down side up to fill up the entire isosceles triangle. 4. We know a equilateral triangle must have three 60°, so the cut away triangle's biggest corner must equals to 360° minus 60° and all of that divided by 2, which is 150°. 5. The final corner to answer this question is equals to 180° minus 150° which is 30°. Thanks to share this interesting puzzle!

[@memesutopia6511]

I thought myself to be a great mathematician, but now i understood that maths requires to be a great magician..........👏👏👏

[@ozzyfromspace]

That was actually really beautiful. I couldn't solve it by geometry either lol. Great video Presh, and awesome explanation!

[@islsl9744]

This is amazing i couldn’t imagine this solution before i watched it!!😍

[@burhan2burhan]

The solution was so easy that my mind stoped working immediately after looking at the question

[@phungpham1725]

Thank you for a nice and elegant solution! My aproach is different. Just label the vertexes of the triangle as A,B,C (A at the right low corner, clockwise). I is the point on AC so that BA= CI. Draw the bisector CH from the vertex C to AB, so angle BCH=ACH=10 degrees From B draw a line forming 60 degees wiht AB , meeting CH at G and AC at F. Now we have the triangle BFC is isosceles (2 bases angles = 20 degrees), and ABG is an equilateral one. Just consider the triangle BFC: BF=FC----> BG+GF=FI+CI----> GF = FI-----> the triangle GFI is an ioscles one, -----> GJ//BC -----> BGIC is a isosceles trapezoid and the line connecting F to the meeting point of BI and CG is also the bisector of the angle BFC and BC. Because of symetric property, BI is the bisector of the angle FBC (compared with the angle FCB), thus FBI = 10 degrees. The angle BFA=180 - (80+60)=40 = angle BIF + 10 Thus Angle BIF= 40-10= 30 degrees

[@kenhaley4]

I did this a different way, also using an equilateral triangle, but it wasn't the first thing I drew. I'll try to explain without a picture, so please label the big triangle vertices A, B, and C with A at the top, and B, C going counter-clockwise. Then label the 4th point D. So AB = CD (given) and AC = BC because the triangle is isosceles, as shown in the video solution. Now construct another isosceles triangle congruent to the big triangle with base at CD and extending upward. Call the vertex of that new triangle E. Now, connect E to A, and it isn't hard to show that AEC is an equilateral triangle. Now look at triangle, AED. That's also isosceles since AE = ED. Angle AED is 40 degrees, as we can subtract the 20 degrees of triangle CED from the 60-degree angle of the equilateral triangle ADE. That means the base angles of the isosceles triangle AED must be 70 ((180 - 40) / 2). So now, we have CDE = 80, EDA = 70, which add to 150. BDC is a straight line (180 degrees), so that leaves angle ADB = 30 degrees, which is the angle we're looking for. Hard to follow the words, but it 's a lot easier if you draw the diagram as you read. I like this solution because it starts by constructing something that makes sense (another isosceles triangle using as a base the side that we know is equal to the base of the original isosceles triangle) rather than arbitrarily drawing the equilateral triangle first. Who would think of doing that...without just getting lucky? Edit (Saturday, 26 Jan 2019): Here's a link to my solution with pictures: drive.google.com/file/d/10y-IbdSMj4gP9IWXFX3tCnO6AS-oEnih/view?usp=sharing

[@derekd.4156]

Ken Haley that’s what I did in my head but I didn’t finish solving it, glad it works!

[@akaRicoSanchez]

If I read this correctly, I did something similar.

[@backseatdog]

Sorry if it's obvious, but how do you show that AEC is an equilateral triangle?

[@sangletan6756]

Sorry for disappointing you but AEC cannot be a equilateral triangle. There is one 60 degrees in it means that it can only be a isoceles triangle( sorry for the bad English I don't really understand the Mathematical term)

[@kenhaley4]

I have two replies challenging the fact that the AEC is equilateral. Here's the proof. ABC and CDE are congruent (constructed). Both are isosceles with angle C = 20 degrees and angle E = 20 degrees. Thus all 4 long sides of these triangles are equal. So, AC = EC. We know that angle ACB is 20 degrees (given) and angle DCE is 80 degrees because it's one of the base angles of the large isosceles triangles. So angle ACE is 60 degrees (80-20). A triangle with two equal sides and with the angle between them of 60 degrees must be equilateral.

[@meshkathossain7066]

I tried for about 1 hour to find that angle. I couldn't do anything out of the ordinary without working inside the triangle. ohh!!! watching your solution I got to realise that I did nothing.

[@laviekolchinsky9441]

Meshkat Hossain Always think "outside the shape" with geometry if nothing inside works. Constructions, constructions, constructions!

[@racimeexe9868]

*same for me i was trying to compute it for more than 1 hour i was only turning around

[@racimeexe9868]

I found many and many solutions to this with a 2 equations and 3 uknowns , but this is not elementary geometry so i failed

[@craiglee6461]

Type this in The Google Translater to english from German: Der Winkel in der oberen linken Ecke ist genau halb so groß wie der 20 grad Winkel, also weiß man jetzt das 10 grad von dem 80 grad Winkel fehlen-> er ist 70 grad groß (der links oben also der der vorher 80 grad Betrug) daher weiß man 70+80=150 und um auf 180 zu kommen +30 -> der Wert des gesuchten Winkels Das habe ich in 5 Minuten im Kopf gemacht :D

[@diegoenrique03]

Yeah that's because schools don't teach you how to use construction

[@dewiasiandaru]

Everytime i saw your video, i'm excited to learn more. Thank u so much.

[@thinhba]

Trời ơi hay quá trời quá đất, nghĩ ra phương án vẽ tam giác đều thật là ngoài sức tưởng tượng, vậy cũng nghĩ ra được. Ko uổng phí khi đăng ký kênh này!!!!

[@ENTERTAININGGAMECHANNEL]

AWESOME VIDEO😀😀😀😀

[@heliamus9605]

daha yeni hem ingilizce anlayabildiğimi hem de geometri yapabildiğimi öğrendim

[@konstantinoskonstantinidis1945]

Classic and awesome geometry problem. Thank you!

[@ashokkumarmishra9687]

Wonderful problem solving! Thank you for sharing

[@bugyborelalle9998]

"Did you figure it out?" aww yesssss... until now I didn't even know the term isosceles triangle in English. :D

[@andycallister8788]

I think I have the simplest solution. Consider the big isosceles triangle ABC, with A top left corner, B right corner and C bottom corner. So in the video, AC is the blue line, and AB and BC are the green lines. Now add a new point internal to the triangle, called D, such that ADC is an equilateral triangle (pointing right). Now draw in the lines AD, BD, and CD. It makes a nice vertically symmetric picture with ABD and CBD being congruent to the inner triangle in the video that had an angle of 20 degrees. From here it is easy to work out all angles from the fact that the original triangle ABC had angles 80 and 20 degrees.

[@whatdaheil]

same 💀 , but I think both solution are simple

[@amananand7579]

Sir, You are doing an excellent job..

[@SotovisionHD]

This is the first math problem form your channel that I could resolveYES !

[@sachinvlogs65]

it's really nice solution

[@harshilpanchal2229]

In these hard puzzles, the hardest is to figure out the construction part

[@SASmit-ht1ch]

Hi Presh Talwarkar, what a fabulously beautiful solution from you to this issue I found the solution with great luck I drew your isosceles triangle on graph paper with a base 8 cm and a high of 23 cm. This simply gave the solution. Anny other ratio does not provide a good solution. Thanks for your clear en good explonation. I'm dutch and 79 and still learning here.. thank again PT

[@ismetlogoglu457]

Unusual question. Expanded my mind.

[@SkiLLsZ]

Im glad this isnt my homework

[@huytrandang277]

It is mine, and fortunately i watched this video

[@amitabhgulati8404]

Lol .. lucky punk..

[@mrityunjaykumar1958]

Today I got this as my homework 😂

[@oguzhan4340]

thanks for Turkish translate good video :)

[@thelastdance8.9]

Greetings from Turkey. I'm very happy to have discovered this channel, I'm enjoying it a lot, I hope it continues like this

[@AnnaKingaB]

It’s brilliant! I’m delighted 🤩🤩🤩

[@TrojaxOnFire]

1:04 lol truly a rare feat

[@AdityaSingh-vx3xo]

Thanks bro

[@riteshpandey8586]

Wowww, even after watching this problem I am unable to figer it out, I will have to see the video more that 3-4 times

[@user-ik6pj5gd2p]

I saw this question while studying Middle school math olympiad, and I knew a tip: when there is 80 80 20 triangle, try to make equilateral triangle. this will help a lot.

[@m_ahtisham]

Him: Did you figure it out? Me:

[@karthikpakki1290]

Beautiful, proves math isn't complicated but fun to try

[@Lillarion]

Below is a very graphical solution that only uses basic math (like knowing that the angle sum in a triangle is 180 degrees). I think you will find it beautiful, and encourage you to draw it for yourself I start out the same as Presh, by identifying that it is indeed an isosceles triangle. Then I too construct an equilateral triangle, but in a different way. I made the observation that 20 is 60/3. It thus makes sense to stack three triangles on top of each other, with the 20 degree sharp corner angles adding up to 60 degrees. By drawing a line through the three triangles, from outer corner to outer corner, you get the equilateral triangle that is showed in the video. If we call the base of one of the three isosceles triangles B, you can now draw a second equilateral triangle with side length B (starting where the angle you should measure is situated). This smaller equilateral triangle will off course have its base (length B) parallel with the base of the larger equilateral triangle. Now comes the magic: If you draw a line that gets you the angle to measure, and draw a mirror-line symmetrically from the other side of the small equilateral triangle you get two lines separated by distance B shooting up and hitting two corners that are also separated by length B (the two corners of the middle one of the three isosceles triangles). It is easy to see (and prove) that both lines shoot up with identical angles from the side of length B in the small equilateral triangle (this is due to symmetry). The ONLY way two lines can start at a line separated by length B, have the same angle, end up at another line, parallel to the first line, and still be separated by a length of B, is if it’s a rectangle. Thus all angles are equal to 90 degrees. Now it is trivial to see that the angle to measure is equal to: 180 - 60 (the angle in the small equilateral triangle) - 90 (the rectangle angle) = 30 degrees. The beauty of this solution is that it’s graphically obvious (if you draw it), and even quite young children would be able to follow the solution.

[@buseft]

This is interesting i couldn't imagine this solution :) Thanks man

[@andrewzhuk8713]

Figured out the angle using Pythagorean theorem before watching the requirement for not using trigonometry. Of course method given here is better, because it is not an easy task to find an arctan from ~0.577 :)

[@naif277]

When i see geometriy.. i sort myself out

[@cmarley314]

Naif Alqarni . When I see geometry, I'm in full retreat in favor of I've cream and a blanket

[@timeonly1401]

Good one!! Love these geometry problems. Thx.

[@hchcey]

Amazing! My high school maths gets fun and cool and super awesome now!

[@muhammadazeemkhan1762]

If elementary geometry includes i.e we can use a+b+c=180 then there are 4 unknowns and 4 equations available which should solve the problem

[@rakeshkumarkavalagi4653]

And I cooked my brains hours together to get this and still couldn't..that was really hard.

[@rahulparit7748]

We can also find out by assuming one of the length then find out remaining lengths and applying cosine rule to find out AD then apply same for angle

[@user-ih1hs7ks6q]

well... after i solve the problem and thought "it must be answer" and i saw the video, he showed quite different solution... .......yeeeaaah i found a new solution

[@kalyanbaidya7339]

This is a very interesting problem. But these kind of problem can be only solved by a fixed construction. So actually it takes a little bit of time.

[@sangletan6756]

Sorry dude but there's a person who has a different way to solve this though :)

[@halukbahadr3029]

when you draw the equilateral triangle upwards and draw a line from the cut point to the new point of the equilateral triangle and baaam It is over. there is a side-by-side equality. 180-80-70=30. It looks easier that way.

[@smithajoseph1374]

20

[@xinfuchen5355]

Marvelous Solution !

[@panyachunnanonda6274]

Thank you, I love your; problem+ solution, very much

[@ProfessorEstrada]

I solved using trigonometry, basically, the sin law. After that I saw the video to check my answer and could know the solution should be Just using elementary geometry. But I can Tell You the trigonometric solution os Also Very cool and It is difficult to "see" the answer is 30 degree because the final expression is strange so that we need to manipulate It.

[@backseatdog]

How do you use the sine law here?

[@user-nh7kc5zp4v]

I got struck in sine cosine equation how did you solve that? SinxSin20-Sin(x-20)Sin80=0 solve this one X is the ans...solve professor

[@Walkerman379]

backseatdog Define the length of the short side of the triangle to be 1. Next cut the triangle in half to form a right triangle with base .5 and angle 80 degree. Use definition of cosine to find the hypotenuse is 2.8794. Now look again at the smaller triangle with the angle we need to solve for. It has known side lengths of 1 and 1.8794. Use Law of cosines to find the other side length as 1.9696. Finally, the Law of Sines tells us that sin(?)=sin(80)/1.9696=.5, so ?= 30 degrees.

[@ProfessorEstrada]

Did You see the file i shared on Dropbox??

[@danvicto]

@@ProfessorEstrada where is this file?

[@liampower2658]

anyone else - not consider this elementary geometry?

[@ertalex9564]

What age are you? Taht is basic tricks, just used in a complex way

[@fitnesschannel1111]

This is elementary

[@matty7834]

Nah that's basic

[@arthurg.machado6803]

Very hard to think, but the properties used were all veery Basic

[@happyhappyguy5034]

just a joke

[@microhoarray]

I watched couple of videos on this channel and i was only able to solve this one. So finally i feel happy

[@guyfisher6574]

My friend and I solved this individually using the Law of Sines and Cosines, given that the ratios of triangle angles to sides must stay constant given any arbitrary side lengths. We arrived at the correct answer, but were quite surprised at this method of solution.

[@haraldhey9210]

Draw the triangle and measure the angle easy.

[@teixeira476]

I'd actually do this if I had to solve it by any means. It's perfectly possible

[@himanshumohanty4220]

You are real gem my brother you took my words💗😂

[@sajithajayachandran9725]

Where the hood where the hood where the hood at!!!???

[@VENOM-tx6gp]

Ami the only one who thinks people who comment some legendry ideas or anything.have a Profile picture (youtube channel image) which seems to be mat Hing with the personality of the comment.

[@labalimbu5153]

haha ..... nice solution

[@brandonfrank3513]

I just did multiple Law of Sins and also one Law of Cosine to find the 30 degree angle

[@snickydoodle4744]

while that is possible and still within my scope of knowledge, it demonstrates my inability to solve problems with foundation

[@dividedshark7511]

@@snickydoodle4744 you could also solve every derivative problem using the limit definition of the derivative but then your boss will fire you for being inefficient.

[@vh73sy]

applying law of sines twice is enough

[@oleksa_corot]

Solved this problem with drawing an equal triangle on the short side of ones, so I get the same result with no coming outside the first triangle. It was hard, thanks for video.

[@durgeshpathak5256]

Wow that was a fantastic question , please make more questions

[@poonamroy5873]

You should post videos more regularly

[@rabbitdrink]

"i like finding lazy people to do hard tasks because theyll find easy ways to do it" -bill gates (quote not exact) ill stick with trig

[@vipinchandra7785]

Ohhh 😁gud

[@whitelittlepanda]

FOR THE FIRST TIME I GOT ONE OF YOUR CHALLENGES RIGHT I'M SO HAPPY

[@sabirekose1601]

This is awesome 👏👏

[@seeker1857]

Who ever has solved it.....salute him....he is a genius This was beyond my imagination

[@user-ey1hf8mw9q]

writer of the question is genius. He/she knows the solution anyhow :)

[@zeynnnn8231]

Cok tesekkurler turkce alt yazi icinnn..💚

[@isminivermekistemeyenmert9358]

Nasıl çözdün acaba

[@ortodontist_kemal]

I have found 30 degree bu myself:) but I should say I solved this problem by a very long method :)) your method is much simpler... congrulations...🙏

[@nntta29]

Very clever solution!

[@chiauthiquynh1671]

It took me half an hour to solve this. I'm not actually that good at math! So happy i was able to solve this by myself! My friends could have done it quicklier i think. Maybe because the math program in my country is heavy as hell 🤦

[@AndrejNikolov-xw2gi]

Did you solve it like the solution?

[@HarnaiDigital]

Turn on full screen and Place a protector on the screen. Easy peasy

[@sipruphothsipruphoth3699]

It’s not always to scale

[@samharper5881]

That only works if your screen is under attack. I suppose you meant protractor.

[@gayatrinage7749]

I was actually gonna do it

[@3bydacreekside]

I think we're in the same boat lol

[@theseeker7194]

@@sipruphothsipruphoth3699 r/wooosh

[@maiaallman4635]

Excellent video!

[@letgodsortm-out1125]

Yes however I had a different method of doing this but I like the different method that u found

[@heartkush4481]

This same question i was saw a few years ago in NCERT EXEMPLAR of class 9 th mathematics in india

[@YasirMahmood7]

Although i studied UP board, i always loved CBSE :)

[@krishnajain2398]

!!

[@kuzeytekinoglu5706]

TOPRAĞININ AKIŞINA ÖLÜRÜM TÜRKİYEM♥️♥️♥️♥️♥️

[@omersarii]

?

[@gurpreetkapoor8993]

I solved this type of problem while proving identity sinA + sinB geometrically, where one angle comes to (A+B)/2 and other one to (A-B) /2 using parallel and perpendicular lines. Method described by u is long. But the required angle in this problem can be solved using only parallel lines and perpendicular lines properties only.

[@thomasaskew1985]

That one took me completely by surprise.

[@EmirhanSanCak]

Bu soru benim problemlerimden daha zorlayıcı çıksa da çözemem iyi günler

[@xtestarossa376]

OMG this reminds me of my middle school life when I was still back in China... Apparently I can't solve this anymore lmao...

[@PlantUp]

It is really a great method!!!😍

[@tchorn2026]

❤️Thanks, Excellent solution! I just signed for your magic channel!!

[@edderiofer]

There are a number of "difficult elementary problems" like this one, all using a 20-80-80 triangle.

[@laviekolchinsky9441]

edderiofer Why that triangle specifically? Is it the properties of isosceles triangle? Is it to do with the specific angles, too?

[@DeepakKumar-gd1wg]

Can you give me some of the links of those problems?

[@edderiofer]

Lavie Kolchinsky It's specifically to do with those angles.

[@nickdsp8089]

Perhaps , because on the side of the triangle where the 80 degrees angles are placed , you can draw an equilateral triangle of 60 degrees angles and the remaining angle of the 80's is 20 which is same as the third angle of the original triangle. This helps a lot to continue solvng the problem

[@cristisprinceana]

beautiful, if there is a God, he likes geometry

[@coguzbes]

Thanks , it is really good