Inside a convex quadrilateral \( ABCD \), a point \( P \) is chosen such that \[ \angle PAD = \angle PAB = \angle PBC = \angle PCB = \angle PDA = 30^\circ. \]Prove that \( \angle CDP = 30^\circ \). Proposed by Vadym Solomka
Source: Kyiv City MO 2025 Round 2, Problem 8.4
Tags: geometry
Inside a convex quadrilateral \( ABCD \), a point \( P \) is chosen such that \[ \angle PAD = \angle PAB = \angle PBC = \angle PCB = \angle PDA = 30^\circ. \]Prove that \( \angle CDP = 30^\circ \). Proposed by Vadym Solomka