In the figure, not drawn to scale, RTUV and QSVW are rhombuses. Given that ∠UTS = 116° and ∠RQW = 122°, find
- ∠QWS
- ∠SWR.
(a)
∠QWS
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle, QW = QR)
(b)
∠SRV
= 180° - 116°
= 64° (Interior angles, UT//VQ)
∠WSQ = ∠QWS = 29° (Isosceles Uriangle, QW = QR)
∠SWR
= 180° - 64° - 29°
= 87° (Angles sum of triangle, WSQ)
Answer(s): (a) 29°; (b) 87°