WAEC - Mathematics (1993 - No. 22)

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

15^o

25^o

40^o

50^o

55^o

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