PQRS is a square. YXR and QXS are straight lines. QP = QY and ∠XQY = 15°. Find
- ∠QPY
- ∠SRY
.
(a)
∠PQS = 45° (Right angle)
∠PQY
= ∠PQS - ∠XQY
= 45° - 15°
= 30°
∠QPY
= (180° - ∠PQY) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
QP = QY = QR
YQR is an isosceles triangle.
∠QYR = ∠QRY (Isosceles triangle)
∠QRY
= (180° - ∠SQR - ∠XQY) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠SRY
= ∠QRS - ∠QRY
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
