Two Methods to Solve for the angle X | (Step-by-step explanation) |

[@abdallahal-khaify]

Thank you alot for simple & good explanation .

[@PreMath]

You are welcome❤️

[@michaelkouzmin281]

Just 1 more (navigator's) solution: let counterclockwise direction be posititive and clockwise - negative and horizontal line =0. So, 0+108-77+110-x=0 (same direction as initial) => x = 141.

[@PreMath]

Thanks ❤️🌹

[@engralsaffar]

That is exactly what I did

[@alexkirchoff5286]

my method was basically the same , but even more naive. I pretended to be driving a car, so at first I turn left by (180 - 108) = 72 ,then right by (180 - 77) = 103 ,then left again by 70 and right by an unknown angle ,but the final direction is the same as initial then sum of turnings left = sum of turning right which gives me a final turn to right by 39° but according to the picture it's required the supplementary angle to this , which is 141. I guess even people from some primitive tribe couldn't find a way simpler than this ☺

[@robertbourke7935]

Nice exercise

[@PreMath]

Yes it is! Thanks ❤️🌹

[@Copernicusfreud]

I just extended the parallel lines on the diagram, and then I drew perpendiculars between the top and bottom parallel lines after I extended the parallel lines to the right. For my method #1, I created two quadrilaterals with angles 72 + 77 + 70 + 141 = 360 and 39 + 90 + 90 + x = 360, so x = 141. For my method #2, I created a triangle and a pentagon. The triangles had angles of 77 + 72 + 31 = 180. The pentagon had angles of 70 + 149 + 90 + 90 + x = 540, so again, x = 141.

[@PreMath]

Thanks ❤️🌹

[@murdock5537]

Nice! fast lane: 108 - 77 + 110 - x = 0 → x = 141

[@PreMath]

Thanks a lot ❤️🌹

[@akramkhanafridi1755]

Well done. Excellent demonstration. Real professional.

[@abdurrahman2008]

thanks it was a nice video ,i am a regular viewer, even though i dont really cmt

[@yalchingedikgedik8007]

Thanks Sir Very easy explained With my glades . ❤❤❤❤

[@arthurschwieger82]

I did two different approaches too and they are different than what you did. The first was to pretend I was walking along the first line and started to add and subtract the navigational moves. My first turn is negative 72°. The next turn is positive 103°. The next turn is negative 70°. The final turn needs to get us back to zero. -72 + 103 - 70 = -39°. Add this to 180° to get X and we have 141°. The other solution was something I remember from way back where the sum of the interior angles and exterior angles should equal because the starting and ending lines are parallel. 108+110-77-X = 0. So 108+110-77 = X = 141. This was a fun one. 🙂

[@arvindarkumar9473]

Great work.... Intresting 😁😁😁 ARVINDAR YADAV India

[@antoniolourenco5277]

Excelente.Obrigado

[@natv8059]

108-77+110-x=0 x=141

[@vadim64841]

Each segment can be described as rotation of the previous segment in clockwise (positive) or anti-clockwise (negative) directions and those rotations just add up to zero at the end. Angle of rotation is computed as 180 minus the angle between the segments. Then the equation is - (180 - 108) + (180 - 77) - (180 - 110) + (180 - x) = 0 Or, cancelling all 180s 108 - 77 + 110 - x = 0 X = 141

[@misterenter-iz7rz]

Extend from angle 108, 110 to form a quadrilateral, then 72+77+70+x=360, x=360-72-77-70=360-219=141.😊

[@PreMath]

Thanks ❤️🌹

[@MrMousley]

Before watching your video, I would do this (and I hope you can understand my method !) The first line and last line are parallel so .. At the 77 degree angle it would take another 31 degrees to get the line coming off it to the right parallel to the first line which means that you would then need add 31 degrees to 110 degrees making the answer 141 degrees.

[@HenrikMyrhaug]

I would say there is a simpler argument for the second method: When the two start and end lines are parallel, the total ammount turned must be equal to 0°. You can also see if you extend each line segment, that the angle turned is 180°-y for all angles with size y in the figure. Because the sum of the turns must be 0°, we get that the sum of turns to the left must be equal to the sum of turns to the right: (180-108)+(180-110)=(180-77)+(180-x) which simplifies to: 108+110=77+x -> 108+110-77=x

[@terrypold]

I think the easiest was to extend the upper right line to the bottom parallel line. The supplement to 110 is 70. The supplement to 108 is 72. 72+77+70=219. 360-219=141.

[@uditproyt5486]

Hey, can you make a video on two unequal chords of the circle which are intersecting each other in the circle, one chord divides into 6,2 then other chord divides into 4,? Conditions: Chords dont meet at 90° Find the radius of the circle Help me please! 😊

[@rakeshkumarrkk5498]

4,3 is that correct

[@ybodoN]

There is not enough information to find the radius (R) of the circle. All we can say is that R ≥ 4 and R ≠ ½√65.

[@uditproyt5486]

@@ybodoN that's an High class olympiad level question that i couldn't solve bruh

[@uditproyt5486]

@@rakeshkumarrkk5498 Each information is correct. You have to find radius not remaining chord

[@grolfe3210]

Similar to the first way, I put in four vertical lines on each of the angles. Easy then to calculate how far each angle is from vertical from left to right.

[@bigm383]

❤😀🥂

[@PreMath]

Thanks a lot ❤️🌹

[@santiagoarosam430]

Consideramos positivos los giros en sentido horario y negativos los antihorarios→ 0+108-77+110-X=0→ X=141º Gracias y saludos.

[@wackojacko3962]

Just for fun , Next time throw a 90⁰ angle in there too ! An angle rarely seen too explain or prove Alternate Angle Theorem. 🙂

[@PreMath]

Thanks ❤️🌹

[@jim55price]

I liked all the terminology that I'd mostly forgotten over the years, but this problem is much easier to solve than using either of the two methods shown here. I solved it in a couple of seconds using 108 - 77 + 110 - x = 0 and then solving for x = 141. Ha ha, now that I've written that out, I see that the very same thing was written here already just 9 days ago. I guess that makes me navigator, too. :)

[@raya.pawley3563]

Thank you

[@PreMath]

You're welcome ❤️🌹

[@BeastModeWorkout24]

Easy

[@gelbkehlchen]

Solution: The horizontal is the scale. The apex angle of 108° is -108° from the horizontal. Then at the next point -108°+77° = -31° from the horizontal. Then at the next point -31°+(180°-110°) = 39° from the horizontal. At the next point, the side angle of x as a step angle is also 39°. And then: x = 39°-180° = -141° from the horizontal. Or unsigned: x = 141°

[@alster724]

I have a 3rd method... On top of the parallelism properties, I used multiple linear pairs and forming triangles and ended up getting 141° as my answer.

[@kenwebster5053]

Taking a clockwise angle to be positive and anticlockwise negative, I get : 108 - 77 + 110 = 141

[@xraymag]

108-77+110=141. Why make it so complicated? This can easily be calculated in the head.

[@Давронжон-л2щ]

After watching this video I can to say answer too.

[@alexandermikhailov2481]

I did the same in my head in 20 seconds before watching the video. 👍

[@fikirfikir3039]

مجموع الزوايا العلوية (108+110=218) تساوي مجموع الزوايا السفلية(77+×=218) ومنه X=141

[@PreMath]

Thanks dear ❤️🌹

[@fikirfikir3039]

@@PreMath Thanks❤

[@thomassr9529]

0 = 108° + 110° -77°- x

[@leehowell7734]

Why not just add the 2 "up" angles (108+110) and subtract the "down" angle 77. I.e. 108+110-77=141

[@comdo777]

asnwer=97 isit

[@giuseppemalaguti435]

X=360-(72+77+70)=360-219=141...basta continuare la retta x/110 fino alla base..

[@mustafacesur9536]

There is an easier way. The sum of the angles pointing upwards is equal to the sum of the angles pointing downwards. X+77°=108°+110°

[@Daniel-qn2mc]

More simply. Two leftward angles of 108° and 110° equal 218°, minus one rightward angle of 77°, equal 218° minus 77°=141° Translated from French to English by Google. Pardon

[@manojitmaity7893]

A simple problem may appear as a hard one like this.

[@krishnakumarramakrishnapil9307]

What u took 108 paralel is actually 108 opposite according to me

[@mihailnaum7642]

108+110=77+× ,x=141

[@JSSTyger]

141

[@Kim-ej2xm]

Arrow concept 108+110=77+x x=141

[@laxmikatta1774]

Day 10 of asking premath sir to reveal his face

[@PreMath]

Hello dear, everything will be revealed once we're prepared for live streaming. You have been heard. You are the best! Thanks ❤️🌹

[@kennethw.edwards1816]

There is a third method: convert the first to azimuth of 90, add 180, add the clockwise angle of 108, subtract 360 give azimuth of 18, then add 180 and subtract the counterclockwise angle of 77 gives azimuth 121, add 180 and add the clockwise angle 110 give azimuth of 51, add 180 to give reverse azimuth of 231, subtract azimuth of last ray of 90 for x equals 141.

[@souravdey7803]

It took me 15 seconds to get the answer😐

[@sivarajkrishna4277]

Why dont this man stop musical elongated English pronunciation

[@mariorossi5857]

x = 108° - 77° + 110° x = 141° (Solved ✓) Is not necessary to draw alternative angles neither parallel lines !!!

[@techlife-101]

truly its not a hard one starting is the key win it

[@anastasiospapaioannou5353]

141