The figure is not drawn to scale. UVY is an equilateral triangle and XVW is an isosceles triangle. WVU and VXZ are straight lines and WU//ZY. ∠YVZ = 90° and ∠XYV = 57°.
- Find ∠WVZ.
- Find ∠VXW.
- Find ∠YXZ.
(a)
∠YVU = 60° (Equilateral triangle UVY)
∠YVZ = 90°
∠XYV = 57°
∠WVZ
= 180° - ∠YVZ - ∠YVU
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠VXW
= (180° - ∠WVZ ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠YXV
= 180° - ∠YVZ - ∠XYV
= 180° - 90° - 57°
= 33°
∠YXZ
= 180° - ∠YXV
= 180° - 33°
= 147° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 147°
