In the diagram above, |PQ| = |QR|, |PS| = |RS|, ∠PSR = 30o and ∠PQR = 80o. Find ∠SPQ.

In the diagram above, |PQ| = |QR|, |PS| = |RS|, ∠PSR = 30^o and ∠PQR = 80^o. Find ∠SPQ.

A.

15^o

B.

25^o

C.

40^o

D.

50^o

E.

55^o

View answer & explanation

Correct answer is B

Join PR
QRP = QPR
= 180 - 80 = ¹⁰⁰/₂₀ = 50^o
SRP = SPR
= 180 - 30 = ¹⁵⁰/₂ = 75^o
∴ SPQ = SPR - QPR
= 75 - 50 = 25^o

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