PQRS is a cyclic quadrilateral with QR as the diameter of the circle. If ∠ SQR = 24°, then what will be the measure of ∠ QPS?

PQRS is a cyclic quadrilateral with QR as the diameter of…

PQRS is a cyclic quadrilateral with QR as the diameter of the circle. If $\angle$ SQR = 24°, then what will be the measure of $\angle$ QPS?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 114°

Given:

$\angle$ SQR = 24°

QR is diameter.

Concept USed:

Sum of the opposite angles of a cyclic quadrilateral is 180°.

Angle subtended by the diameter of a circle to its circumference is 90°.

Explanation:

According to the given question,

Now, In triangle QRS, $\angle$ QSR + $\angle$ SRQ + $\angle$ SQR = 180°

⇒ 90° + $\angle$ SRQ + 24° = 180°

⇒ $\angle$ SRQ = 66°

Also, in cyclic quadrilateral PQRS, $\angle$ QPS + $\angle$ QRS = 180°

⇒ $\angle$ QPS = 180° - 66°

⇒ $\angle$ QPS = 114°

Hence the required answer is 114°.