Answer: C
The formula for tangent is tan(x)= opposite/ adjacent so plugging it in would be tan(x)=9/4
Choice C, because

So it's less than what she originally had (which isn't possible)
Your diagram is correct.
I would have however written the Given as stated
Given :
XB≅XA≅AY≅YB ( If they are equidistant then they are all the same distance, thus the values will all be equal)
Prove:
<x≅<b≅<y≅<a (this is because a square is formed) < is angle
XM≅YM≅AM≅MB (The fact that the previous statements are true means that this is a square, if M is the midpoint than all these segments are equal)
MX≅MY
Im not sure what you did wrong besides maybe you didn't prove it well enough, everything is correct that you have written. I cant read the pen but it looks like you were missing a step.
Answer:
Prove that KL is equal to c by Pythagorean Theorem.
Step-by-step explanation:
In the two triangles triangle KLM is a right triangle with sides a and b as the two legs of the right triangle .We can apply Pythagorean Theorem to find KL.
In triangle KGF two sides are a and b .If we prove KL=EF then Pythagorean Theorem will be true for triangle KGF and hence we can prove triangle KGF to be a right triangle.
The correct option to prove triangle KGF to be a right triangle is to Prove that KL is equal to c by Pythagorean Theorem.