FGHJ is a square. NMH and GMJ are straight lines. GF = GN and ∠MGN = 15°. Find
- ∠GFN
- ∠JHN
.
(a)
∠FGJ = 45° (Right angle)
∠FGN
= ∠FGJ - ∠MGN
= 45° - 15°
= 30°
∠GFN
= (180° - ∠FGN) ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(b)
GF = GN = GH
NGH is an isosceles triangle.
∠GNH = ∠GHN (Isosceles triangle)
∠GHN
= (180° - ∠JGH - ∠MGN) ÷ 2
= (180° - 45° -15°) ÷ 2
= 120° ÷ 2
= 60°
∠JHN
= ∠GHJ - ∠GHN
= 90° - 60°
= 30°
Answer(s): (a) 75°; (b) 30°
