In the figure, not drawn to scale, KMNP and JLPQ are rhombuses. Given that ∠NML = 117° and ∠KJQ = 126°, find
- ∠JQL
- ∠LWK.
(a)
∠JQL
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle, JQ = JR)
(b)
∠LKP
= 180° - 117°
= 63° (Interior angles, NM//PQ)
∠QLJ = ∠JQL = 27° (Isosceles Nriangle, JQ = JR)
∠LWK
= 180° - 63° - 27°
= 90° (Angles sum of triangle, WLQ)
Answer(s): (a) 27°; (b) 90°