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 = 46° and ∠RNS = 31°. Find
- ∠KNM
- ∠NQP
(a)
∠KNS
= (180° - 46°) ÷ 2
= 67° (Isosceles triangle)
∠KNM
= 180° - 67°
= 113° (Angles on a straight line)
(b)
∠QNP
= 67° - 31°
= 36°
∠NQP
= (180° - 36°) ÷ 2
= 72 ° (Isosceles triangle)
Answer(s): (a) 113°; (b) 72°