Question

❑ PQRS is a cyclic quadrilateral in which m∠SQR = 65 and m∠QPR = 30, then m∠QRS = ______
(a) 85
(b) 95
(c) 115
(d) 150

Answer 1

∠QRS = 85 degrees

Step-by-step explanation:

Rules applied

1) In a cyclic quadrilateral, sum of opposite angles = 180 degrees

2) Angles in the same segment in a cyclic quadrilateral are equal

Given ∠SQR = 65 degrees and ∠QPR = 30 degrees

From rule 2, considering SR is the line segment, ∠SQR =  ∠SPR = 65 degrees

So ∠SPQ = ∠SPR + ∠RPQ = 65 degrees + 30 degrees = 95 degrees

From rule 1, ∠QRS + ∠SPQ = 180 degrees

i.e. 95 + ∠QRS  = 180 degrees

So, ∠QRS = 85 degrees