The figure is not drawn to scale. XYB is an equilateral triangle and AYZ is an isosceles triangle. ZYX and YAC are straight lines and ZX//CB. ∠BYC = 90° and ∠ABY = 59°.
- Find ∠ZYC.
- Find ∠YAZ.
- Find ∠BAC.
(a)
∠BYX = 60° (Equilateral triangle XYY)
∠BYC = 90°
∠ABY = 59°
∠ZYC
= 180° - ∠BYC - ∠BYX
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠YAZ
= (180° - ∠ZYC ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠BAY
= 180° - ∠BYC - ∠ABY
= 180° - 90° - 59°
= 31°
∠BAC
= 180° - ∠BAY
= 180° - 31°
= 149° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 149°
