The figure is not drawn to scale. Triangle FGE is an isosceles triangle. Triangle CDE is an equilateral triangle. ∠GEF is
15 of ∠DCE and ∠DEG = ∠CEF.
- Find ∠DEG.
- Find ∠CFE.
(a)
∠DEC = 60° (Equilateral triangle)
∠GEF
= ∠DEC x
15 = 60° x
15 = 12°
∠DEG = ∠CEF
∠DEG
= ∠DEC - ∠GEA) ÷ 2
= (60° - 12°) ÷ 2
= 48° ÷ 2
= 24° (Isosceles triangle)
(b)
∠CFE
= 180° - ∠DCE - ∠DEG
= 180° - 60° - 24°
= 96° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 96°