In the figure, HJKL is a trapezium and HLMQ is a rhombus. HL is parallel to JK and LM = LN. QLK and LPN are straight lines. ∠LHQ = 41° and ∠PLQ = 33°. Find
- ∠HLK
- ∠LNM
(a)
∠HLQ
= (180° - 41°) ÷ 2
= 69.5° (Isosceles triangle)
∠HLK
= 180° - 69.5°
= 110.5° (Angles on a straight line)
(b)
∠NLM
= 69.5° - 33°
= 36.5°
∠LNM
= (180° - 36.5°) ÷ 2
= 71.75 ° (Isosceles triangle)
Answer(s): (a) 110.5°; (b) 71.75°