Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>Use rhombus $A B C D$ with $m \angle 1=2 x+20, m \angle 2=5 x-4$, $A C=15,$ and $m \angle 3=y^{2}+26 .$ 
Find AF