The figure is not drawn to scale. TUWX is a square and STX is an equilateral triangle. UVW is an isosceles triangle. SWV is a straight line.
- Find ∠XSW.
- Find ∠UVW.
(a)
∠WXT = 90°
∠SXT = 60° (Equilateral triangle SXB)
∠SXW
= 90° + 60°
= 150°
∠XSW
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠SWU
= 90° - ∠SWX;
= 90° - 15°
= 75°
∠VWU
= 180° - ∠SWU
= 180° - 75°
= 105° (Angles on a straight line)
∠UVW
= (180° - ∠VWC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
