The figure is not drawn to scale. Triangle DEC is an isosceles triangle. Triangle ABC is an equilateral triangle. ∠ECD is
15 of ∠BAC and ∠BCE = ∠ACD.
- Find ∠BCE.
- Find ∠ADC.
(a)
∠BCA = 60° (Equilateral triangle)
∠ECD
= ∠BCA x
15 = 60° x
15 = 12°
∠BCE = ∠ACD
∠BCE
= ∠BCA - ∠ECA) ÷ 2
= (60° - 12°) ÷ 2
= 48° ÷ 2
= 24° (Isosceles triangle)
(b)
∠ADC
= 180° - ∠BAC - ∠BCE
= 180° - 60° - 24°
= 96° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 96°