Two tangents AP and AQ are drawn to a circle with center O from an external point A, where P and Q are points on the circle.  If ∠PAQ = 80°, then ∠AOP is equal to?

50°

∠PAQ = 80°, and

∠P and ∠Q = 90° 

In the case of tangent ⇒ line OA bisect the angles ∠PAQ and ∠POQ.

Therefore,

In Δ PAO:

∠P = 90°, ∠PAO = 40°, so ∠PAO = 90° - 40° = 50°