In the figure, NPQR is a trapezium and NRSV is a rhombus. NR is parallel to PQ and RS = RT. VRQ and RUT are straight lines. ∠RNV = 52° and ∠URV = 33°. Find
- ∠NRQ
- ∠RTS
(a)
∠NRV
= (180° - 52°) ÷ 2
= 64° (Isosceles triangle)
∠NRQ
= 180° - 64°
= 116° (Angles on a straight line)
(b)
∠TRS
= 64° - 33°
= 31°
∠RTS
= (180° - 31°) ÷ 2
= 74.5 ° (Isosceles triangle)
Answer(s): (a) 116°; (b) 74.5°