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PQRS is a cyclic quadrilateral with ∠ $P = (x + 20)$ °, ∠ $Q = (2 x - 10)$ ° and ∠ $R = (3 x - 20)$ °. Find ∠S.

Competition practiceGeometry

A100°
B80°
C115°
D65°

Step-by-Step Solution

∠P + ∠

R = 180

°, so

4 x = 180

and

x = 45

. Then ∠

Q = 80

° and ∠

S = 180° - 80° = 100°

.

Answer: A) 100°

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