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 = 43° and ∠URV = 30°. Find
- ∠NRQ
- ∠RTS
(a)
∠NRV
= (180° - 43°) ÷ 2
= 68.5° (Isosceles triangle)
∠NRQ
= 180° - 68.5°
= 111.5° (Angles on a straight line)
(b)
∠TRS
= 68.5° - 30°
= 38.5°
∠RTS
= (180° - 38.5°) ÷ 2
= 70.75 ° (Isosceles triangle)
Answer(s): (a) 111.5°; (b) 70.75°