The figure is not drawn to scale. Triangle ABZ is an isosceles triangle. Triangle XYZ is an equilateral triangle. ∠BZA is
25 of ∠YXZ and ∠YZB = ∠XZA.
- Find ∠YZB.
- Find ∠XAZ.
(a)
∠YZX = 60° (Equilateral triangle)
∠BZA
= ∠YZX x
25 = 60° x
25 = 24°
∠YZB = ∠XZA
∠YZB
= ∠YZX - ∠BZA) ÷ 2
= (60° - 24°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
(b)
∠XAZ
= 180° - ∠YXZ - ∠YZB
= 180° - 60° - 18°
= 102° (Angles sum of triangle)
Answer(s): (a) 18°; (b) 102°