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 = 49° and ∠RNS = 25°. Find
- ∠KNM
- ∠NQP
(a)
∠KNS
= (180° - 49°) ÷ 2
= 65.5° (Isosceles triangle)
∠KNM
= 180° - 65.5°
= 114.5° (Angles on a straight line)
(b)
∠QNP
= 65.5° - 25°
= 40.5°
∠NQP
= (180° - 40.5°) ÷ 2
= 69.75 ° (Isosceles triangle)
Answer(s): (a) 114.5°; (b) 69.75°