The figure is not drawn to scale. VWYZ is a square and UVZ is an equilateral triangle. WXY is an isosceles triangle. UYX is a straight line.
- Find ∠ZUY.
- Find ∠WXY.
(a)
∠YZV = 90°
∠UZV = 60° (Equilateral triangle UZB)
∠UZY
= 90° + 60°
= 150°
∠ZUY
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠UYW
= 90° - ∠UYZ;
= 90° - 15°
= 75°
∠XYW
= 180° - ∠UYW
= 180° - 75°
= 105° (Angles on a straight line)
∠WXY
= (180° - ∠XYC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
