The figure is not drawn to scale. TUX is an equilateral triangle and WUV is an isosceles triangle. VUT and UWY are straight lines and VT//YX. ∠XUY = 90° and ∠WXU = 54°.
- Find ∠VUY.
- Find ∠UWV.
- Find ∠XWY.
(a)
∠XUT = 60° (Equilateral triangle TUY)
∠XUY = 90°
∠WXU = 54°
∠VUY
= 180° - ∠XUY - ∠XUT
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠UWV
= (180° - ∠VUY ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠XWU
= 180° - ∠XUY - ∠WXU
= 180° - 90° - 54°
= 36°
∠XWY
= 180° - ∠XWU
= 180° - 36°
= 144° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 144°
