In the figure, not drawn to scale, QSTU and PRUV are rhombuses. Given that ∠TSR = 117° and ∠QPV = 126°, find
- ∠PVR
- ∠RWQ.
(a)
∠PVR
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle, PV = PR)
(b)
∠RQU
= 180° - 117°
= 63° (Interior angles, TS//UQ)
∠VRP = ∠PVR = 27° (Isosceles Triangle, PV = PR)
∠RWQ
= 180° - 63° - 27°
= 90° (Angles sum of triangle, WRQ)
Answer(s): (a) 27°; (b) 90°