The figure is not drawn to scale. Triangle DEC is an isosceles triangle. Triangle ABC is an equilateral triangle. ∠ECD is
35 of ∠BAC and ∠BCE = ∠ACD.
- Find ∠BCE.
- Find ∠ADC.
(a)
∠BCA = 60° (Equilateral triangle)
∠ECD
= ∠BCA x
35 = 60° x
35 = 36°
∠BCE = ∠ACD
∠BCE
= ∠BCA - ∠ECA) ÷ 2
= (60° - 36°) ÷ 2
= 24° ÷ 2
= 12° (Isosceles triangle)
(b)
∠ADC
= 180° - ∠BAC - ∠BCE
= 180° - 60° - 12°
= 108° (Angles sum of triangle)
Answer(s): (a) 12°; (b) 108°