Question 2
Let $I$ be the incenter of a triangle $ABC$, and $D$ be the point of intersection of $AI$ with the circumcircle of $ABC$. Let $M$ be the midpoint of $AD$, and $E$ be the point of the segment $BD$ such that $IE$ is perpendicular to $BD$. If $IB + IE = \frac{AD}{2}$, $ME$ is parallel to $AB$, and the point $M$ is inside the segment $AI$, determine the measure of the angles of the triangle $ABC$.