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 = 41° and ∠RNS = 31°. Find
- ∠KNM
- ∠NQP
(a)
∠KNS
= (180° - 41°) ÷ 2
= 69.5° (Isosceles triangle)
∠KNM
= 180° - 69.5°
= 110.5° (Angles on a straight line)
(b)
∠QNP
= 69.5° - 31°
= 38.5°
∠NQP
= (180° - 38.5°) ÷ 2
= 70.75 ° (Isosceles triangle)
Answer(s): (a) 110.5°; (b) 70.75°