Question

PQRS is a cyclic quadrilateral such that PR is a diameter of the circle. If ∠QPR=67° and ∠SPR=72°, then ∠QRS=
A. 41°
B. 23°
C. 67°
D. 18°

Answer 1

Hope this helps u dear......

Answer 2

Given : PQRS is a cyclic quadrilateral such that PR is a diameter of the circle  and ∠QPR = 67° and ∠SPR = 72°.

To find : ∠QRS

Solution :  

∠SPQ = ∠QPR + ∠SPR

∠SPQ = 67° + 72°

∠SPQ = 139°

Since, PQRS is a cyclic quadrilateral, and Sum of Opposite pair of angles in a  cyclic quadrilateral is 180° :  

∠SPQ + ∠QRS = 180°  

139° + ∠QRS = 180°

∠QRS = 180° - 139°  

∠QRS = 41°

Hence, ∠QRS is 41°.

Among the given options option (A)  41° is correct.

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