Given a pentagon $ABCDE$ with all its interior angles less than $180^\circ$. Prove that if $\angle ABC = \angle ADE$ and $\angle ADB = \angle AEC$, then $\angle BAC = \angle DAE$.
Source: IMONST2 2022 Senior #4
Tags: geometry, Angle Chasing, polygon
Given a pentagon $ABCDE$ with all its interior angles less than $180^\circ$. Prove that if $\angle ABC = \angle ADE$ and $\angle ADB = \angle AEC$, then $\angle BAC = \angle DAE$.