In the figure above, what is the value of x?

[u.gmat]

The answer is 70 but can I get the reasoning for it? Image attached.

Thanks.

http://postimage.org/image/pzf47ui9x/bf0ff39a/

[sfbay]

three triangles Left Middle Right
left is 3-4-5
right is 5-12-13
*these are common Pythagorean triples - you should memorize*

middle is 5-5-who cares (ok u can solve easily using Pythagorean but no need)
since equal sides it is isosceles which also means equal angles (opposite equal sides). sum of angles in M= 180= x+55+55 solve for M

[tim]

this is correct, except for the fact that you can't solve for the third side using the pythagorean theorem. there are no mathematical techniques used on the GMAT that will allow you to solve for the missing side, but as you mentioned it's irrelevant anyway since all we need is the angle..

[sfbay]

yep, did not need it so it was a throw away statement i did not give much thought.

however going beyond GMAT math you could draw an altitude from X angle to unknown side splitting the isosceles triangle and use cosine etc

[jnelson0612]

yep, did not need it so it was a throw away statement i did not give much thought.

however going beyond GMAT math you could draw an altitude from X angle to unknown side splitting the isosceles triangle and use cosine etc

Fortunately you will never have to use cosines on the GMAT! :-)