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>If $\overline{GH} \cong \overline{HK}$, $\overline{HJ} \cong \overline{YK}$, and $m \angle GJK=100$, what is the measure of $\angle HGK$ ?