The figure is not drawn to scale. STVW is a square and RSW is an equilateral triangle. TUV is an isosceles triangle. RVU is a straight line.
- Find ∠WRV.
- Find ∠TUV.
(a)
∠VWS = 90°
∠RWS = 60° (Equilateral triangle RWB)
∠RWV
= 90° + 60°
= 150°
∠WRV
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠RVT
= 90° - ∠RVW;
= 90° - 15°
= 75°
∠UVT
= 180° - ∠RVT
= 180° - 75°
= 105° (Angles on a straight line)
∠TUV
= (180° - ∠UVC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
