World's hardest easy problem

1. Sep 3, 2013

2. Sep 3, 2013

janhaa

I haven't the solution, I get the equation x + y = 130, where x and y are angles. If $x, y \in Z^+$
This is a diophantine equation. We know: x, y > 0. y > x. And y is greater than 90 degrees.
the most probable angles:
$x=20^o\,\, ,y=110^o$
or
$x=30^o\,\, ,y=100^o$

Last edited: Sep 3, 2013
3. Sep 3, 2013

reenmachine

I tried a couple of things but didn't solve it yet , but there's probably a way to build your way up to the x angle using the tricks in my sketch (just don't have the patience to construct the triangles properly and doing it now):

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Last edited: Sep 3, 2013
4. Sep 3, 2013

Integral

Staff Emeritus
Simple geometry is all that is required.

Why can't you do this for yourself? Don't give up so easy.

5. Sep 4, 2013

namanjain

wazz it,
well i need an approach
i asked it to one of my faculty at coaching and he straightaway said it's wrong so i needed to check

6. Sep 4, 2013

namanjain

whatss y in equation
x+y= 130

reenmachine i agree myself i even not have patience and doing it (doing angle sum property question) , thanks for tip of parallel lines but what benefit it does

7. Sep 4, 2013

reenmachine

I don't know since I didn't solve it.It was just a suggestion of strategy to attack the problem , maybe it's a dead end , but the parallel lines will at least allow you to chase more angles , whether or not they end up being useful to find angle x.

If you don't have the patience to try it , I suggest you do not ask others to do it for you as it's not recommended on the forum to ask for answers without showing that you tried hard before hand.I'm not a moderator , just friendly advice.Also , saying that you tried hard is not showing that you tried hard.

Last edited: Sep 4, 2013
8. Sep 4, 2013

namanjain

till here i ve done (in attchment)
one of image is inverted
so i did the mirror image from webcam toy

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9. Sep 4, 2013

reenmachine

You should draw the triangles/angles to scale if you want to try that strategy.

It should look like the picture below

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Last edited: Sep 4, 2013
10. Sep 4, 2013

namanjain

however i got that but i also meant that diophtine (whatever is name) equation

well where is it taught

Last edited by a moderator: May 6, 2017
11. Sep 4, 2013

namanjain

does that help, because doing any of olympiads we were never told to draw to scale and i was always of kind to do geometry of this kind mentally so it's quite difficult for me
though i think i'll print that page

12. Sep 4, 2013

namanjain

Uff! After long work with a correct precise figure i bored and saw solution on one of other web pages

is it bad of me not getting it (i'm 15 yrs and preparing rmo and iit)

13. Sep 4, 2013

reenmachine

I don't know , you should listen to your teachers before you listen to me that's for sure :tongue2:

You should also listen to mentors here as they are qualified to help you.

Last edited: Sep 4, 2013
14. Sep 4, 2013

reenmachine

Might try to prove both of these triangles (or another pair of triangles) are similar to prove x = 20 :

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Last edited: Sep 4, 2013