PQRS is a square. WVR and QVS are straight lines. QP = QW and ∠VQW = 15°. Find
- ∠QPW
- ∠SRW
.
(a)
∠PQS = 45° (Right angle)
∠PQW
= ∠PQS - ∠VQW
= 45° - 15°
= 30°
∠QPW
= (180° - ∠PQW) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
QP = QW = QR
WQR is an isosceles triangle.
∠QWR = ∠QRW (Isosceles triangle)
∠QRW
= (180° - ∠SQR - ∠VQW) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠SRW
= ∠QRS - ∠QRW
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
