PQRS is a parallelogram. PA bisects angle P and SA bisects angle S

Geometry

In the figure given below, PQRS is a parallelogram. PA bisects angle P and SA bisects angle S. What is angle PAS equal to?

  1. 60°
  2. 75°
  3. 90°
  4. 100°

Answer

Since PQRS is a parallelogram,

∠P + ∠S = 180°

PA bisects ∠P and SA bisects ∠S,

∠PSA + ∠APS = 180°/2 = 90°

In the triangle PAS

∠PAS + ∠PSA + ∠APS = 180°

∠PAS = 180° - 180°/2 = 90°

The correct option is C.