In the figure, KLMN is a trapezium and KNPS is a rhombus. KN is parallel to LM and NP = NQ. SNM and NRQ are straight lines. ∠NKS = 52° and ∠RNS = 31°. Find
- ∠KNM
- ∠NQP
(a)
∠KNS
= (180° - 52°) ÷ 2
= 64° (Isosceles triangle)
∠KNM
= 180° - 64°
= 116° (Angles on a straight line)
(b)
∠QNP
= 64° - 31°
= 33°
∠NQP
= (180° - 33°) ÷ 2
= 73.5 ° (Isosceles triangle)
Answer(s): (a) 116°; (b) 73.5°