A) aas theorem b) asa postulate c) sas postulate d) sss postulate

I am not sure so don't hate me if this is wrong but I think its AAS.

It is the angle-angle-side (AAS) Theorem, or choice (A)

This is because the triangles share one side implying its length is equal fro the two triangles. Besides that, the triangles are share two of same angles: they are both right-angled and <V=<Y. The latter implies Similarity. Combined with one side of each triangle being of same length implies Congruence.  

step-by-step explanation:

the ratio of red paint to blue paint is always 9/7. that means that, whatever x's value, (4x+12)/(4x-4) has that same ratio. so, set up an equation and cross-multiply to solve for x:

9/7 = (4x+12)/(4x-4)

9(4x-4) = 7(4x+12)

36x - 36 = 28x + 84

8x - 36 = 84

8x = 120

x = 15