NPQR is a square. UTQ and PTR are straight lines. PN = PU and ∠TPU = 15°. Find
- ∠PNU
- ∠RQU
.
(a)
∠NPR = 45° (Right angle)
∠NPU
= ∠NPR - ∠TPU
= 45° - 15°
= 30°
∠PNU
= (180° - ∠NPU) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
PN = PU = PQ
UPQ is an isosceles triangle.
∠PUQ = ∠PQU (Isosceles triangle)
∠PQU
= (180° - ∠RPQ - ∠TPU) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠RQU
= ∠PQR - ∠PQU
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
