The figure is not drawn to scale. QRU is an equilateral triangle and TRS is an isosceles triangle. SRQ and RTV are straight lines and SQ//VU. ∠URV = 90° and ∠TUR = 57°.
- Find ∠SRV.
- Find ∠RTS.
- Find ∠UTV.
(a)
∠URQ = 60° (Equilateral triangle QRY)
∠URV = 90°
∠TUR = 57°
∠SRV
= 180° - ∠URV - ∠URQ
= 180° - 90° - 60°
= 30° (Angles on a straight line)
(b)
∠RTS
= (180° - ∠SRV ÷ 2
= (180° - 30°) ÷ 2
= 150° ÷ 2
= 75° (Isosceles triangle)
(c)
∠UTR
= 180° - ∠URV - ∠TUR
= 180° - 90° - 57°
= 33°
∠UTV
= 180° - ∠UTR
= 180° - 33°
= 147° (Angles on a straight line)
Answer(s): (a) 30°; (b) 75°; (c) 147°
