In the diagram, |SP| = |SR| and < PRS = 50o. Calculate < PQR

Mathematics

WAEC 2007

In the diagram, |SP| = |SR| and < PRS = 50^o. Calculate < PQR

A. 120^o
B. 110^o
C. 100^o
D. 80^o

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Correct Answer: Option C

Explanation

< PRS = RPS = 50^o (base of isosceles)

RPS = 50^o; < RSP + < PRS + < RPS = 180(sum of < s in a triangle)

< RPS + 50 + 50 = 180

< RSP = 180 - 100 = 80

then < PQR + < RSp = 180 (opp. < S of cyclic quad.)

< PQR + 80 = 180^o

< PQR = 180 - 80

= 100

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