The figure is not drawn to scale. STW is an equilateral triangle and VTU is an isosceles triangle. UTS and TVX are straight lines and US//XW. ∠WTX = 90° and ∠VWT = 57°.
- Find ∠UTX.
- Find ∠TVU.
- Find ∠WVX.
(a)
∠WTS = 60° (Equilateral triangle STY)
∠WTX = 90°
∠VWT = 57°
∠UTX
= 180° - ∠WTX - ∠WTS
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠TVU
= (180° - ∠UTX ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠WVT
= 180° - ∠WTX - ∠VWT
= 180° - 90° - 57°
= 33°
∠WVX
= 180° - ∠WVT
= 180° - 33°
= 147° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 147°
