World's Hardest Easy Geometry Problem

[Crystal Cuckoo]

I think I may have stumbled onto the world's hardest easy geometry problem:

http://thinkzone.wlonk.com/MathFun/Triangle.htm

You must find x (or a in the diagram), but only using basic geometry rules (so no trigonometry).
And you can't just measure it, either. That's just cheating.

Here's the scale diagram:

http://thinkzone.wlonk.com/MathFun/Triangle1Hint0.htm

So, run along, my fellow Escapists, and decide whether you can solve it or not.

 

[PersianLlama]

Bleh, I hated Geometry, I'll try to remember my rules and solve this after I eat breakfast.

 

[neolithic]

40 deg. I think, it's early, and stuff is still fuzzy.

and on second look, I'm pretty sure I'm wrong. but, I hated proofs, anyways, I'm off to make waffles.

 

[wewontdie11]

Pretty sure it's 40.

 

[Nimbus]

COuld you guys show your workings? "Pics or it didn't happen".

 

[Limasol]

Its just cunningly set up so you have to work out about 6 other angles before a, it doesn't make it hard, just annoying.

 

[Nimbus]

Its just cunningly set up so you have to work out about 6 other angles before a, it doesn't make it hard, just annoying.

I actually worked out all the angles, and stil couldn't get A. You definatly need to do something different, I'm just not sure what...

 

[aleczm]

I'm honestly not sure what the answer is. however, if the triangle with A is a right triangle, the answer is 40.

i wouldn't be surprised if it is not.

 

[Laughing Man]

Solution below

http://madcap_2000_chat.homestead.com/files/solution.jpg

 

[TheRightToArmBears]

It is 40. Sorry, I'm too lazy to type up why. And The calculator on windows is crap.

 

[NeutralDrow]

Solution below

http://madcap_2000_chat.homestead.com/files/solution.jpg

How did you get the angles for triangle CDE?

 

[AssassinX66]

Its 40. This was extremely easy for me since I'm doing similair stuff right now.

 

[Mayonegg]

Its just cunningly set up so you have to work out about 6 other angles before a, it doesn't make it hard, just annoying.

This. You've got use basic rules of what adds up to 180/360 degrees as well as the law of opposite angles being the same ('X' angles if you like). Then create bigger triangles from the smaller ones and then you get 40. Thought it sure doesn't look like 40 in the diagram.

Anyway, nice puzzle, it's nice to go back to maths every so often.

 

[iJosh]

Done.
/Thread.

True that. That's what I was going to do, but you saved me a bunch of time.

 

[NeutralDrow]

Its just cunningly set up so you have to work out about 6 other angles before a, it doesn't make it hard, just annoying.

This. You've got use basic rules of what adds up to 180/360 degrees as well as the law of opposite angles being the same ('X' angles if you like). Then create bigger triangles from the smaller ones (i.e. ignoring the smaller ones) and then you get 40. Thought it sure doesn't look like 40 in the diagram.

Anyway, nice puzzle, it's nice to go back to maths every so often.

But how? I figured out the angles of seven different triangles and one quadrilateral, and still couldn't do it. How does one get the angles CDE and CED? I could figure out the larger angles using the unnamed point in the middle, but I couldn't split them out of 180*...

 

[ElephantGuts]

That's the kind of stuff that made me probably fail a quiz yesterday. Stop rubbing it in, I feel bad enough already.

 

[Red Right Hand]

Its just cunningly set up so you have to work out about 6 other angles before a, it doesn't make it hard, just annoying.

This. You've got use basic rules of what adds up to 180/360 degrees as well as the law of opposite angles being the same ('X' angles if you like). Then create bigger triangles from the smaller ones and then you get 40. Thought it sure doesn't look like 40 in the diagram.

Anyway, nice puzzle, it's nice to go back to maths every so often.

It's not 40, it's 20, I just don't know how you get that, though 20 is 100% correct

 

[Mayonegg]

So sorry, I've just come in. You have to make parallel lines to the largest equal sides of the triangle to create new triangles, then you know they're parallel, therefore equal('Z' angles)

NB: I really am terrible at explaining maths.

 

[Falru]

From a purely stupid-man's point of view, that angle looks wayyy too acute to be 40, 20 seems more likely.