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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°
Solution
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°
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