The figure is not drawn to scale. Triangle ABZ is an isosceles triangle. Triangle XYZ is an equilateral triangle. ∠BZA is
15 of ∠YXZ and ∠YZB = ∠XZA.
- Find ∠YZB.
- Find ∠XAZ.
(a)
∠YZX = 60° (Equilateral triangle)
∠BZA
= ∠YZX x
15 = 60° x
15 = 12°
∠YZB = ∠XZA
∠YZB
= ∠YZX - ∠BZA) ÷ 2
= (60° - 12°) ÷ 2
= 48° ÷ 2
= 24° (Isosceles triangle)
(b)
∠XAZ
= 180° - ∠YXZ - ∠YZB
= 180° - 60° - 24°
= 96° (Angles sum of triangle)
Answer(s): (a) 24°; (b) 96°