Question 1
In $\triangle ABC$ with $AB = AC,$ point $D$ lies strictly between $A$ and $C$ on side $\overline{AC},$ and point $E$ lies strictly between $A$ and $B$ on side $\overline{AB}$ such that $AE = ED = DB = BC.$ The degree measure of $\angle ABC$ is $\frac{m}{n},$ where $m$ and $n$ are relatively prime positive integers. Find $m + n.$