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 = 45° and ∠RNS = 33°. Find
- ∠KNM
- ∠NQP
(a)
∠KNS
= (180° - 45°) ÷ 2
= 67.5° (Isosceles triangle)
∠KNM
= 180° - 67.5°
= 112.5° (Angles on a straight line)
(b)
∠QNP
= 67.5° - 33°
= 34.5°
∠NQP
= (180° - 34.5°) ÷ 2
= 72.75 ° (Isosceles triangle)
Answer(s): (a) 112.5°; (b) 72.75°