NPQR is a square. VUQ and PUR are straight lines. PN = PV and ∠UPV = 11°. Find
- ∠PNV
- ∠RQV
.
(a)
∠NPR = 45° (Right angle)
∠NPV
= ∠NPR - ∠UPV
= 45° - 11°
= 34°
∠PNV
= (180° - ∠NPV) ÷ 2
= (180° - 34°) ÷ 2
= 146° ÷ 2
= 73° (Isosceles triangle)
(b)
PN = PV = PQ
VPQ is an isosceles triangle.
∠PVQ = ∠PQV (Isosceles triangle)
∠PQV
= (180° - ∠RPQ - ∠UPV) ÷ 2
= (180° - 45° -11°) ÷ 2
= 124° ÷ 2
= 62°
∠RQV
= ∠PQR - ∠PQV
= 90° - 62°
= 28°
Answer(s): (a) 73°; (b) 28°
