Mathematics
In the given figure, RT is a tangent touching the circle at S. If ∠PST = 30° and ∠SPQ = 60°, then ∠PSQ is :
40°
30°
60°
90°
Answer
We know that,
Angle between tangent and the chord at the point of contact is equal to angle of the alternate segment.
∴ ∠PQS = ∠PST = 30°
In △ PQS,
By angle sum property of triangle,
⇒ ∠PQS + ∠QPS + ∠PSQ = 180°
⇒ 30° + 60° + ∠PSQ = 180°
⇒ ∠PSQ + 90° = 180°
⇒ ∠PSQ = 180° - 90° = 90°.
Hence, option 4 is the correct option.
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