The figure is not drawn to scale. Triangle BCA is an isosceles triangle. Triangle YZA is an equilateral triangle. ∠CAB is
25 of ∠ZYA and ∠ZAC = ∠YAB.
- Find ∠ZAC.
- Find ∠YBA.
(a)
∠ZAY = 60° (Equilateral triangle)
∠CAB
= ∠ZAY x
25 = 60° x
25 = 24°
∠ZAC = ∠YAB
∠ZAC
= ∠ZAY - ∠CAA) ÷ 2
= (60° - 24°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
(b)
∠YBA
= 180° - ∠ZYA - ∠ZAC
= 180° - 60° - 18°
= 102° (Angles sum of triangle)
Answer(s): (a) 18°; (b) 102°