In the figure, not drawn to scale. QRST is a square. STU is an equilateral triangle and QS is a straight line. Find
- Two-thirds of ∠QVU
- Twice of ∠USV
(a)
∠TQS = 45° (Right angle)
∠VTS = 60° (Equilateral triangle)
∠QTV
= 90° - ∠VTS
= 90° - 60°
= 30°
∠QVU
= 30° + 45° (Exterior angle of a triangle)
= 75°
Two-thirds of ∠QVU
=
23 x 75°
= 50°
(b)
∠UVS
= 180° - ∠QVU
= 180° - 75°
= 105° (Angles on a straight line)
∠USV
= 180° - 60° - 105°
= 15° (Angles sum of triangle)
Twice of ∠USV
= 2 x 15°
= 30°
Answer(s): (a) 50°; (b) 30°
