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>Find $m \widehat{E D B}$ if $m \widehat{F E}=118, m \widehat{A B}=108$, $m \angle E G B=52,$ and $m \angle E F B=30$.