The figure is not drawn to scale. Triangle DEC is an isosceles triangle. Triangle ABC is an equilateral triangle. ∠ECD is
25 of ∠BAC and ∠BCE = ∠ACD.
- Find ∠BCE.
- Find ∠ADC.
(a)
∠BCA = 60° (Equilateral triangle)
∠ECD
= ∠BCA x
25 = 60° x
25 = 24°
∠BCE = ∠ACD
∠BCE
= ∠BCA - ∠ECA) ÷ 2
= (60° - 24°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
(b)
∠ADC
= 180° - ∠BAC - ∠BCE
= 180° - 60° - 18°
= 102° (Angles sum of triangle)
Answer(s): (a) 18°; (b) 102°