In the figure, not drawn to scale, JLMN and HKNP are rhombuses. Given that ∠MLK = 117° and ∠JHP = 126°, find
- ∠HPK
- ∠KWJ.
(a)
∠HPK
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle, HP = HR)
(b)
∠KJN
= 180° - 117°
= 63° (Interior angles, ML//NQ)
∠PKH = ∠HPK = 27° (Isosceles Mriangle, HP = HR)
∠KWJ
= 180° - 63° - 27°
= 90° (Angles sum of triangle, WKQ)
Answer(s): (a) 27°; (b) 90°