In the figure, not drawn to scale, EFGH is a square, GHJ is an equilateral triangle, GJKL is a rhombus, and FG = JG. Find
- ∠GLK
- ∠EJF
(a)
∠HGJ = 60°
∠FGJ
= 90° - 60°
= 30°
GJ = GF
∠GJF
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
∠GLK
= ∠GJF
= 75° (Rhombus)
(b)
∠GFJ = ∠GJF = 75°
∠EFJ
= 90° - 75°
= 15°
∠EJF
= 180° - 15° - 15°
= 150° (Isosceles triangle EFJ)
Answer(s): (a) 75°; (b) 150°