In the figure, not drawn to scale, KMNP and JLPQ are rhombuses. Given that ∠NML = 120° and ∠KJQ = 122°, find
- ∠JQL
- ∠LWK.
(a)
∠JQL
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle, JQ = JR)
(b)
∠LKP
= 180° - 120°
= 60° (Interior angles, NM//PQ)
∠QLJ = ∠JQL = 29° (Isosceles Nriangle, JQ = JR)
∠LWK
= 180° - 60° - 29°
= 91° (Angles sum of triangle, WLQ)
Answer(s): (a) 29°; (b) 91°