Question 15
In the triangle $ABC$ shown in the diagram below, the external angle bisectors of $\angle B$ and $\angle C$ meet at $D$. The tangent from $D$ to the incircle $\omega$ of triangle $ABC$ touches $\omega$ at $E$, where $E$ and $B$ are on the same side of line $AD$. Suppose $\angle BEC=112^\circ$. Find the size of $\angle A$ in degrees.
