In the given figure, AP is perpendicular to BC, and AQ is the bisector of angle PAC. What will be the measure of angle PAQ ?

45° 30° 50° 60°

30°

We know that, In ΔAPC, AP ⊥ BC = ∠APC = 90°  ∠ACP = 30°  = ∠PAC = 180° - (∠APC + ∠ACP) = ∠PAC = 180° - (90° + 30°) = 60°  We also know that, AQ is the angle bisector of ∠PAC =∠PAQ = ∠CAQ = ∠PAQ = 60°/2 = 30°