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 = 40° and ∠RNS = 33°. Find
- ∠KNM
- ∠NQP
(a)
∠KNS
= (180° - 40°) ÷ 2
= 70° (Isosceles triangle)
∠KNM
= 180° - 70°
= 110° (Angles on a straight line)
(b)
∠QNP
= 70° - 33°
= 37°
∠NQP
= (180° - 37°) ÷ 2
= 71.5 ° (Isosceles triangle)
Answer(s): (a) 110°; (b) 71.5°