A quadrilateral PQRS is inscribed in a circle of centre O, such that PQ is a diameter and . Find the value of .
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 30°.
PQRS is a cyclic quadrilateral and PQ is the diameter of the circle.
∠PSR = 120°
The sum of opposite angles of the cyclic quadrilateral is 180°.
The sum of all internal angles of a triangle is 180°.
The angle subtended by a diameter on any point of a circle is 90°.
∠RQP = 180° - ∠PSR = 180° - 120° = 60°
Here, ∠PRQ = 90°
In ΔPRQ, ∠QPR + ∠RQP + ∠PRQ = 180°
⇒ ∠QPR + 60° + 90° = 180°
⇒ ∠QPR = 180° - 150° = 30°
Therefore, the measure of ∠QPR is 113°.