The figure is not drawn to scale. Triangle BCA is an isosceles triangle. Triangle YZA is an equilateral triangle. ∠CAB is
35 of ∠ZYA and ∠ZAC = ∠YAB.
- Find ∠ZAC.
- Find ∠YBA.
(a)
∠ZAY = 60° (Equilateral triangle)
∠CAB
= ∠ZAY x
35 = 60° x
35 = 36°
∠ZAC = ∠YAB
∠ZAC
= ∠ZAY - ∠CAA) ÷ 2
= (60° - 36°) ÷ 2
= 24° ÷ 2
= 12° (Isosceles triangle)
(b)
∠YBA
= 180° - ∠ZYA - ∠ZAC
= 180° - 60° - 12°
= 108° (Angles sum of triangle)
Answer(s): (a) 12°; (b) 108°