The figure is not drawn to scale. JLMN is a trapezium and JL // NM. Given that JN = JK, ∠NJK = 72° and ∠JLM = 97°.
- Find ∠LMN
- Find ∠JKN
- Find ∠KNM
(a)
∠LMN
= 180° - 97°
= 83° (Interior angles, JL//NM)
(b)
∠JKN
= (180° - 72°) ÷ 2
= 108° ÷ 2
= 54° (Isosceles triangle)
(c)
∠KNM
= ∠JKN
= 54° (Alternate angles, JL//NM)
Answer(s): (a) 83°; (b) 54°; (c) 54°