Question

In the given figure, a measure of ∠POQ is…..

Answer 1

PQ is tangent to circle and OP is radius

⇒ ∠OPQ= 90° …radius is perpendicular to tangent

⇒ ∠PQO = 30° …given

Consider ΔOPQ

⇒ ∠OPQ + ∠PQO + ∠POQ = 180° …sum of angles of triangle

⇒ 90° + 30° + ∠POQ = 180°

⇒ 120° + ∠POQ = 180°

⇒ ∠POQ = 60°

Hence ∠POQ is 60°