In the figure, not drawn to scale, MPQR and LNRS are rhombuses. Given that ∠QPN = 114° and ∠MLS = 126°, find
- ∠LSN
- ∠NWM.
(a)
∠LSN
= (180° - 126°) ÷ 2
= 54 ÷ 2
= 27° (Isosceles triangle, LS = LR)
(b)
∠NMR
= 180° - 114°
= 66° (Interior angles, QP//RQ)
∠SNL = ∠LSN = 27° (Isosceles Qriangle, LS = LR)
∠NWM
= 180° - 66° - 27°
= 87° (Angles sum of triangle, WNQ)
Answer(s): (a) 27°; (b) 87°