In the figure, not drawn to scale, NQRS and MPST are rhombuses. Given that ∠RQP = 116° and ∠NMT = 122°, find
- ∠MTP
- ∠PWN.
(a)
∠MTP
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle, MT = MR)
(b)
∠PNS
= 180° - 116°
= 64° (Interior angles, RQ//SQ)
∠TPM = ∠MTP = 29° (Isosceles Rriangle, MT = MR)
∠PWN
= 180° - 64° - 29°
= 87° (Angles sum of triangle, WPQ)
Answer(s): (a) 29°; (b) 87°