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 = 42° and ∠URV = 34°. Find
- ∠NRQ
- ∠RTS
(a)
∠NRV
= (180° - 42°) ÷ 2
= 69° (Isosceles triangle)
∠NRQ
= 180° - 69°
= 111° (Angles on a straight line)
(b)
∠TRS
= 69° - 34°
= 35°
∠RTS
= (180° - 35°) ÷ 2
= 72.5 ° (Isosceles triangle)
Answer(s): (a) 111°; (b) 72.5°