In the figure, not drawn to scale, MPQR and LNRS are rhombuses. Given that ∠QPN = 116° and ∠MLS = 124°, find
- ∠LSN
- ∠NWM.
(a)
∠LSN
= (180° - 124°) ÷ 2
= 56 ÷ 2
= 28° (Isosceles triangle, LS = LR)
(b)
∠NMR
= 180° - 116°
= 64° (Interior angles, QP//RQ)
∠SNL = ∠LSN = 28° (Isosceles Qriangle, LS = LR)
∠NWM
= 180° - 64° - 28°
= 88° (Angles sum of triangle, WNQ)
Answer(s): (a) 28°; (b) 88°