The figure is not drawn to scale. UVXY is a square and TUY is an equilateral triangle. VWX is an isosceles triangle. TXW is a straight line.
- Find ∠YTX.
- Find ∠VWX.
(a)
∠XYU = 90°
∠TYU = 60° (Equilateral triangle TYB)
∠TYX
= 90° + 60°
= 150°
∠YTX
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠TXV
= 90° - ∠TXY;
= 90° - 15°
= 75°
∠WXV
= 180° - ∠TXV
= 180° - 75°
= 105° (Angles on a straight line)
∠VWX
= (180° - ∠WXC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
