MathNet 2007-part-02 — 187 problems (EN–VI) Question 4

Let $ABCD$ be a convex quadrilateral with $\angle DAC = \angle BDC = 36^\circ$, $\angle CBD = 18^\circ$ and $\angle BAC = 72^\circ$. The diagonals $AC$ and $BD$ intersect at point $P$. Determine the measure of $\angle APD$.