In the figure, not drawn to scale, FGHJ is a square, HJK is an equilateral triangle, HKLM is a rhombus, and GH = KH. Find
- ∠HML
- ∠FKG
(a)
∠JHK = 60°
∠GHK
= 90° - 60°
= 30°
HK = HG
∠HKG
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠HML
= ∠HKG
= 75° (Rhombus)
(b)
∠HGK = ∠HKG = 75°
∠FGK
= 90° - 75°
= 15°
∠FKG
= 180° - 15° - 15°
= 150° (Isosceles triangle FGK)
Answer(s): (a) 75°; (b) 150°