In the figure, not drawn to scale, QSTU and PRUV are rhombuses. Given that ∠TSR = 114° and ∠QPV = 122°, find
- ∠PVR
- ∠RWQ.
(a)
∠PVR
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle, PV = PR)
(b)
∠RQU
= 180° - 114°
= 66° (Interior angles, TS//UQ)
∠VRP = ∠PVR = 29° (Isosceles Triangle, PV = PR)
∠RWQ
= 180° - 66° - 29°
= 85° (Angles sum of triangle, WRQ)
Answer(s): (a) 29°; (b) 85°