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 = 47° and ∠URV = 34°. Find
- ∠NRQ
- ∠RTS
(a)
∠NRV
= (180° - 47°) ÷ 2
= 66.5° (Isosceles triangle)
∠NRQ
= 180° - 66.5°
= 113.5° (Angles on a straight line)
(b)
∠TRS
= 66.5° - 34°
= 32.5°
∠RTS
= (180° - 32.5°) ÷ 2
= 73.75 ° (Isosceles triangle)
Answer(s): (a) 113.5°; (b) 73.75°