PQRS is a square. KJR and QJS are straight lines. QP = QK and ∠JQK = 11°. Find
- ∠QPK
- ∠SRK
.
(a)
∠PQS = 45° (Right angle)
∠PQK
= ∠PQS - ∠JQK
= 45° - 11°
= 34°
∠QPK
= (180° - ∠PQK) ÷ 2
= (180° - 34°) ÷ 2
= 146° ÷ 2
= 73° (Isosceles triangle)
(b)
QP = QK = QR
KQR is an isosceles triangle.
∠QKR = ∠QRK (Isosceles triangle)
∠QRK
= (180° - ∠SQR - ∠JQK) ÷ 2
= (180° - 45° -11°) ÷ 2
= 124° ÷ 2
= 62°
∠SRK
= ∠QRS - ∠QRK
= 90° - 62°
= 28°
Answer(s): (a) 73°; (b) 28°
