NPQR is a square. HGQ and PGR are straight lines. PN = PH and ∠GPH = 15°. Find
- ∠PNH
- ∠RQH
.
(a)
∠NPR = 45° (Right angle)
∠NPH
= ∠NPR - ∠GPH
= 45° - 15°
= 30°
∠PNH
= (180° - ∠NPH) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
PN = PH = PQ
HPQ is an isosceles triangle.
∠PHQ = ∠PQH (Isosceles triangle)
∠PQH
= (180° - ∠RPQ - ∠GPH) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠RQH
= ∠PQR - ∠PQH
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
