Which one is the right answer?

D

Step-by-step explanation:

First of all, i mean A and B are out first thing because you don't have enough information to find out if it's true.

C is incorrect because as stated before, not enough information.

However,

You know that the angles 1-8 are all supplementary, which means that 1 and 2 can be added to make 180 degrees, as so can 3 and 4, 3 and 1. 2 and 4, blah blah blah.

In D, the angles that are being added are supplementary, because the three lines making up that weird figure is adjacent and is parallel to each other.

If you give one of the angles a degree, you know that 180-x with x being that degree, will equal the other angle on the other side of the lines.

Therefore its D.

Edit:

I just realized that theres an angle stated at the top of the screen. Still with that angle given, A and B is incorrect and the answer is still D.

geometry: triangles

solvers

lessons

answers archive

call the larger triangle abc

then the smaller triangle cde is similar to abc (all angles are equal, aaa).  

ab is the side that is 36, and we wish to find de, the side corresponding to ab

area_cde = area_abc - area_cde --> area_abc / area_cde = 2

let x=length of de

ratio of areas = (ratio of sides)^2

+2+=+%2836%2fx%29%5e2+

+2+=+1296%2fx%5e2+

++x%5e2+=+1296%2f2+=+648+

25.45584