Question

PQRS is a cyclic quadrilateral with QR as the diameter of the circle. If ∠SQR = 24°, then what will be the measure of ∠QPS?
1. 114°
2. 126°
3. 104°
4. 116°

Answer 1

Correct Answer - Option 1 : 114°

Given:

∠SQR = 24° 

Calculation:

∠QRS = 90° (Angle inscribed in a semicircle)

⇒ ∠SQR + ∠QRS + ∠RSQ = 180° [sum of interior angles of a triangle is 180°]

⇒ 24° + 90° + ∠RSQ = 180° 

⇒ 114° + ∠RSQ = 180° 

⇒ ∠RSQ = (180° – 114°)

⇒ ∠RSQ = 66° 

Now,

∠QPS + ∠RSQ = 180° [sum of pair of opposite sides of cyclic quadrilateral is 180°]

⇒ ∠QPS + 66° = 180° 

⇒ ∠QPS = (180° – 66°)

⇒ ∠QPS = 114° 

∴ The required value of ∠QPS is 114°