In the figure, not drawn to scale, RTUV and QSVW are rhombuses. Given that ∠UTS = 113° and ∠RQW = 126°, find
- ∠QWS
- ∠SWR.
(a)
∠QWS
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle, QW = QR)
(b)
∠SRV
= 180° - 113°
= 67° (Interior angles, UT//VQ)
∠WSQ = ∠QWS = 27° (Isosceles Uriangle, QW = QR)
∠SWR
= 180° - 67° - 27°
= 86° (Angles sum of triangle, WSQ)
Answer(s): (a) 27°; (b) 86°