NPQR is a square. WVQ and PVR are straight lines. PN = PW and ∠VPW = 11°. Find
- ∠PNW
- ∠RQW
.
(a)
∠NPR = 45° (Right angle)
∠NPW
= ∠NPR - ∠VPW
= 45° - 11°
= 34°
∠PNW
= (180° - ∠NPW) ÷ 2
= (180° - 34°) ÷ 2
= 146° ÷ 2
= 73° (Isosceles triangle)
(b)
PN = PW = PQ
WPQ is an isosceles triangle.
∠PWQ = ∠PQW (Isosceles triangle)
∠PQW
= (180° - ∠RPQ - ∠VPW) ÷ 2
= (180° - 45° -11°) ÷ 2
= 124° ÷ 2
= 62°
∠RQW
= ∠PQR - ∠PQW
= 90° - 62°
= 28°
Answer(s): (a) 73°; (b) 28°
