Question

HELPP!! GEOMETRY!!!

Answer 1

@strenesmee
Can you find all three angles of triangle DEF in terms of a, x, y and z?
hint: use the exterior angle property.

Answer 2

D=a+z, E= a+x, F=a+y

Answer 3

Excellent!
Can you write these angles on the figure, and then examine the angles?

Answer 4

Do you see similar triangles?

Answer 5

DEF & ABC are similar

Answer 6

Can you complete the question from here?

Answer 7

Where do you find such simple yet tricky problems ?

Answer 8

9/27=8/AB --- AB=24
thanks i could not see the similarity

Answer 9

Excellent!
As @ganeshie8 said, this is a very nice problem, different from most of the rest!

Answer 10

Yes, they are real beauties. I solved one yesterday for strenesmee, very tricky indeed

Answer 11

where the devil do you get them from?

Answer 12

@strenesmee

Just like the other problem, can you deduce all the other angles in terms of a, b and c, write them down, and look for similarities?

Answer 13

I have to go now, but will be back to check on your progress.

Answer 14

@alekos

The angle (c-b) is derived as follows
angle = 180-2(a+b) ................sum of angles of a triangle
=180-(2a+b)-b........................algebraic rearranglement
=(180-2a-b)-b......................... rearrangement
=c-b........................................sum of angles of a triangle
So angle BAD=angle C.
Now you can continue the search for similar triangles!