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.

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[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.

[orenaharoni]

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

[nicolasortiz]

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

[shototodoroki]

Problem: Alright, solve for this angle.

Solution: Create multiple triangles until you get what you want

[panagiotisdeligiannis]

Anyone: I feel very confident of my math skills.

Presh: Can you solve this problem that was given to newborns in China?

[vankrelian]

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

[manshisinha]

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

[jsfbr]

This solution demands tons of experience with geometry.

[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.

[atulchauhan]

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

[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.

[yogeshsharma]

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

[Sam-psxs]

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

[feşTR-]

Türkçe alt yazıyı yapandan Allah razı olsun. ❤

[annettemeyer]

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.

[allisonfisher]

This looked much easier that it was...

[UltraSexyChipotle]

Video: don't use trigonometry

Me: no

[mathdetectivej]

Another langley problem!

Have a nice day!

[schino]

well... using a protractor is elementary geometry too

[hydra]

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.