PSLEUVWX is a parallelogram, UWY is an equilateral triangle and WX = XY.
- Find ∠UWX.
- Find ∠WXU.
- Find ∠YUV.
(a)
WX = XY
Triangle WXY is an isosceles triangle.
∠XWY
= (180° - 144°) ÷ 2
= 36° ÷ 2
= 18° (Isosceles triangle)
∠UWX
= 60° - 18°
= 42° (Equilateral triangle)
(b)
∠UYX
= 60° - 18°
= 42° (Equilateral triangle)
∠UXY
= 180° - 42° - 18°
= 120° (Angles sum of triangle)
∠UXW
= 360° - 144° - 120°
= 96° (Angles at a point)
∠VUW
= ∠UWX
= 42° (Alternate angles)
∠VUY
= 60° + 42°
= 102°
Answer(s): (a) 42°; (b) 96°; (c) 102°