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[Haly]

You can find the answer easily simply by drawing the triangle with a protractor. The real problem lies in deducing the answer using only the basic angle/triangle laws.

 

[ProfessorLobo]

You can find the answer easily simply by drawing the triangle with a protractor. The real problem lies in deducing the answer using only the basic angle/triangle laws.

I figured it out easily and all I had to do was type it into Google.

 

[XiaNaphryz]

I figured it out easily and all I had to do was type it into Google.

 

[Jake.]

this thread makes me feel dumb.

 

[DanteFox]

ok so I looked up the answer and I don't see how any "elementary" geometry student could possibly solve this problem.

A warning to anyone that is valiantly still trying to solve this: Don't bother. The solution involves around 20 steps of drawing extra lines and equating those lines and their respective angles with the original lines and angles. I don't see how anyone could possibly, logically begin drawing those lines in the triangle, given that there are numerous possible lines to be drawn inside the triangle. We won't think any less of you if you look up the solution. tl;dr It's a dumb problem

 

[XiaNaphryz]

ok so I looked up the answer and I don't see how any "elementary" geometry student could possibly solve this problem.

Good to admit you didn't read the OP then with the author's note at the bottom.

How hard are these problems? Any teenage student and some younger students can understand the proof, but very very few are able to discover the proof on their own. Of the hundreds of people that have emailed me, I'd estimate only one or two percent (mostly math professionals and college students) have solved it without significant hints.

 

[DanteFox]

Good to admit you didn't read the OP then with the author's note at the bottom.

I did read that but it's just dumb. No matter who you are, you'd have to have some crazy geometric logic in order to solve it, or just get lucky drawing random lines around. Either that or there's some higher level thinking process that makes it as easy and systematic as solving a linear equation or something.

edit: In order to scare off anyone who is still trying, I'll post a link to the final diagram with all the extra lines. If you see this, and have the problem spoiled for you because you were just about to go about solving it in this manner, you have my apologies and my admiration, but odds are you'll be spared a lot of pointless frustration.

click at your own risk (and for your own sanity)!!!
http://lh6.ggpht.com/_nHKMHCatCf8/R1V479M5qRI/AAAAAAAAAUw/uzbexhvFtNY/s512/Triangle6.png

 

[Feep]

I did read that but it's just dumb. No matter who you are, you'd have to have some crazy geometric logic in order to solve it, or just get lucky drawing random lines around. Either that or there's some higher level thinking process that makes it as easy and systematic as solving a linear equation or something.

I agree that the solution (that I found, anyway) is extremely inelegant. You're not going to have this sudden burst of clarity and exclaim, "Ah-ha!" It's tedious. Still, I find it interesting that a solvable problem like this could be so almost arbitrarily difficult.

 

[Revengeance]

I spent about an hour and a half on this this afternoon. My attempt involved lots of parallel lines and bisecting lines, and I gave up once my desk started looking like something from A Beautiful Mind.

I might give it another go tomorrow. Or I might just break out the google.

 

[ninjarr]

I didn't quite finish the problem, but the path I was taking was very similar to the solution posted above (draw the lines which make the corner triangles congruent, then look at the triangle formed at the intersection's angles). I don't think it is at all outlandish to say it is doable. I was a bit disappointed that I didn't finish it after going in the right direction though, but its Spring Bring, its my time off!