Question

In the given diagram RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is equal to ______.

Options

• 40°

• 30°

• 60°

• 90°

Answer 1

In the given diagram RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is equal to 90°.

Explanation:

∠PQS = ∠PST   ...(∠S in alternate segment)

= 30°

In ΔPQS,

∠PQS + ∠PSQ + ∠SPQ = 180°

30° + ∠PSQ + 60° = 180°

∠PSQ = 180° – 90°

= 90°