In the figure, not drawn to scale, JLMN and HKNP are rhombuses. Given that ∠MLK = 120° and ∠JHP = 122°, find
- ∠HPK
- ∠KWJ.
(a)
∠HPK
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle, HP = HR)
(b)
∠KJN
= 180° - 120°
= 60° (Interior angles, ML//NQ)
∠PKH = ∠HPK = 29° (Isosceles Mriangle, HP = HR)
∠KWJ
= 180° - 60° - 29°
= 91° (Angles sum of triangle, WKQ)
Answer(s): (a) 29°; (b) 91°