3 angles in a triangle are x, 2x and (x - 32) degrees - what are the actual angles in degrees?

[@Ayelmar]

Solved at the thumbnail, the answer is b) 53, 106, 21. Since the angles of any triangle sum to 180, and given the three angles are x, 2x, and x-32, let's write the equation as follows: 0) X + 2x + (x-32) = 180 -- starting positition 1) 4x - 32 = 180 -- combine terms 2) 4x = 180 + 32 -- add 32 to both sides 3) 4x = 212 -- (continued) 4) x = 53, and thus 2x = 106 and x-32 = 21

[@HR-wd6cw]

As long as we keep in mind that the sum of the angles in a triangle is 180 degrees we use that to figure out x and thus calculate each angle. So: 180 = x + 2x + (x - 32), simplified it would be 212 = 4x (we move the -32 to the other side so it's added to 180 to get 212 on the other side of the equation, and we divide by 4). And since we know the sum of angles in a triangle has to be 180 degrees, we can also check our work and make sure the answer is correct. (Now, answer C would technically fit the fact that the sum of all angles is 180, but when you fill in the numbers for "x" it doesn't make sense, same for "d". "a" is obviously wrong since they don't even add up to 180.

[@dazartingstall6680]

Ignoring that b is the only choice which even makes sense... 4x − 32 = 180 4x = 212 x = 53 2x = 106 x − 32 = 21

[@denisewenke8323]

B. No other answer has one number that's double one of the others.

[@brothaantone8286]

I’m glad I subscribed.

[@Hi-rw8vr]

Only one of the options works with the x+2x+x-32. Maybe make better options that all follow the rule, but don’t add up to 180?

[@Serisky621]

I agree!!! It is much too easy to eliminate all wrong answers. Or maybe make it NOT multiple choice.

[@aryusure1943]

I'm glad I was right to study algebra before geometry. :) But this one was easy as long as you know that the sum of the angles of a triangle is 180 degrees and that you know how to figure out 2x in a multiple choice problem.

[@robertlawson8572]

"I'm glad I was right to study algebra before geometry. :)" You got a choice? I didn't! Though... we were learning Algebra without knowing it at my school. How? Given the prices and quantities of various grocery items, we were tasked with working out a total cost. The sneaky thing was, we were encouraged to use abbreviations for the items. Apples = a, Bananas = b, Cucumbers = c. 3a + 4b + 2c = ? Simple algebraic notation disguised as shorthand...

[@aryusure1943]

@@robertlawson8572 Fun way to be introduced to algebra. As for me I was talking about my new adventure in maths. I don't remember what we studied first when I was in school.

[@robertlawson8572]

@@aryusure1943 It wasn't clear that you were referring to a more recent learning experience than you'd had in your school days... Anyway the use of algebraic notation in place of writing "apples" or "bananas" appealed to my naturally lazy nature. I thought the teacher's method was deceptively clever... (in retrospect)

[@janelbrookshire7011]

I got a smiley face, 100%, a certificate and a gold star? 🥳

[@richardl6751]

Yes you did and a high five.

[@Usmctbone]

I canceled c&d, then a. You can look at the angles and see that 2 of the 3 are acute but nowhere close to the same angle (the obtuse angle gave that away so both couldn't be 30°).

[@winstonm9764]

Haven’t watched the video yet, so I’m going to say that the angles are 53°, 106°, and 21°.

[@richardhole8429]

Done in my head. 4x - 32 = 180 4x = 212 x = 53 D

[@andrewmovius1654]

B is the only answer that meets the x-32 unknown angle: x-32 CANNOT = x

[@panlomito]

The total degrees of a triangle is 180° (always), we find us here a sum of (x-32) + x +2x=180 or 4x = 212 No calculator of course, that is only for smart kids... 2x = 106 -> x = 53° So the answer will be 21, 106 and 53° but not one of the multiple choice answer is even close so I must be wrong.

[@tomtke7351]

x° + 2x° + (x - 32)° = 180°

[@tomtke7351]

b) because 106 = 2×53

[@russelllomando8460]

Got it B 4X = 212 thanks for the fun

[@andrewsniimensaamoo253]

The answer is B , 53+106+21

[@mimimiraj7351]

I looked at the picture of the angle..(2x)... I looked at the answers 106 stood out

[@charlesmitchell5841]

B) 53, 106, 21?

[@ChrisLichowicz]

God! Every angle on a triangle will add up to 180 degrees, people. He says algebra. I did with addition.

[@josephlaura7387]

b) 53,106,21 degrees

[@Lee-ku6lk]

B. Is the Correct Answer

[@kevingeier3385]

You are correct.

[@davidwatson7604]

Algo boost! Generally speaking Boom

[@bravewave2084]

B. I plugged in the answers after eliminating A.

[@wernerviehhauser94]

No need for algebra since there is only one solution with a difference of 32 between the numbers.

[@robhaver8704]

it can only be answer B 'cause 2x is x times 2 = 53 times 2 = 106

[@hakopajemyan334]

53 106 20

[@deograciousuwiragiye8429]

I can choose b.

[@leladeliyannis8674]

53

[@harrymatabal8448]

Wtf one angle is outside the diagram

[@boryanaspasova4372]

B is the correct answer

[@Jeanne90275]

b)

[@jimrattley1372]

B obviously

[@jsEMCsquared]

B without reading the comments obvious 73 er 53

[@terry_willis]

Pieces cake.

[@patriciapederson3134]

B

[@kennethwright870]

Clearly b

[@KartarHoonjan]

b

[@mauriziograndi1750]

b) obviously because add up to 180 degrees on the contrary of the other answers.

[@Serisky621]

Answer is b), but c) & d) also add to 180. By the way, please write more clearly, with better grammar.

[@mauriziograndi1750]

Yes I realised afterwards that also the others angles were adding up to 180 degrees. I was in a hurry because occurred to me before that some answers were very obvious and and I found them at a glance by inspection. But thanks to have pointed that out.

[@mauriziograndi1750]

b)

[@RonaldPower-b8z]

b

[@carolfoster6863]

B

[@amanraj8827]

B

[@MrBobWingard]

B

[@samswift4921]

B