The figure is not drawn to scale. WXA is an equilateral triangle and ZXY is an isosceles triangle. YXW and XZB are straight lines and YW//BA. ∠AXB = 90° and ∠ZAX = 56°.
- Find ∠YXB.
- Find ∠XZY.
- Find ∠AZB.
(a)
∠AXW = 60° (Equilateral triangle WXY)
∠AXB = 90°
∠ZAX = 56°
∠YXB
= 180° - ∠AXB - ∠AXW
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠XZY
= (180° - ∠YXB ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠AZX
= 180° - ∠AXB - ∠ZAX
= 180° - 90° - 56°
= 34°
∠AZB
= 180° - ∠AZX
= 180° - 34°
= 146° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 146°
