In the figure, not drawn to scale, NQRS and MPST are rhombuses. Given that ∠RQP = 119° and ∠NMT = 124°, find
- ∠MTP
- ∠PWN.
(a)
∠MTP
= (180° - 124°) ÷ 2
= 56 ÷ 2
= 28° (Isosceles triangle, MT = MR)
(b)
∠PNS
= 180° - 119°
= 61° (Interior angles, RQ//SQ)
∠TPM = ∠MTP = 28° (Isosceles Rriangle, MT = MR)
∠PWN
= 180° - 61° - 28°
= 91° (Angles sum of triangle, WPQ)
Answer(s): (a) 28°; (b) 91°