The figure is not drawn to scale. RSV is an equilateral triangle and UST is an isosceles triangle. TSR and SUW are straight lines and TR//WV. ∠VSW = 90° and ∠UVS = 57°.
- Find ∠TSW.
- Find ∠SUT.
- Find ∠VUW.
(a)
∠VSR = 60° (Equilateral triangle RSY)
∠VSW = 90°
∠UVS = 57°
∠TSW
= 180° - ∠VSW - ∠VSR
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠SUT
= (180° - ∠TSW ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠VUS
= 180° - ∠VSW - ∠UVS
= 180° - 90° - 57°
= 33°
∠VUW
= 180° - ∠VUS
= 180° - 33°
= 147° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 147°
