The figure is not drawn to scale. RSUV is a square and QRV is an equilateral triangle. STU is an isosceles triangle. QUT is a straight line.
- Find ∠VQU.
- Find ∠STU.
(a)
∠UVR = 90°
∠QVR = 60° (Equilateral triangle QVB)
∠QVU
= 90° + 60°
= 150°
∠VQU
= (180° - 150°) ÷ 2
= 30° ÷ 2
= 15° (Isosceles triangle)
(b)
∠QUS
= 90° - ∠QUV;
= 90° - 15°
= 75°
∠TUS
= 180° - ∠QUS
= 180° - 75°
= 105° (Angles on a straight line)
∠STU
= (180° - ∠TUC) ÷ 2
= (180° - 105°) ÷ 2
= 75° ÷ 2
= 37.5° (Isosceles triangle)
Answer(s): (a) 15°; (b) 37.5°
