Geometry Practice Test 7

∠ABC = 100°
ABCD is a concyclic quadrilateral

∠D + ∠B = 180°
(sum of two opposite angles of a concyclic quadrilateral is 180°.)
∠D + 100 = 180°
∠D = 180° - 100°
∠D = 80°
∠DAP = ∠DCA = 80°
(∵ alternative interior segment property)
In ΔACP,
∠ACP + ∠PAC + ∠CPA = 180°
∠APC = 180° - (80° + 80°)
∠APC = 20°