In the figure, NPQR is a parallelogram. QT, TU and NP are straight lines. NRS is an isosceles triangle.
- Find ∠t.
- Find ∠v.
(a)
∠QTN = ∠PNU = 62° (Corresponding angles, NP//TQ)
∠TSN
= 180° - ∠QTN - ∠TNS
= 180° - 62° - 20°
= 98° (Angles sum of triangle)
∠RSN
= 180° - 98°
= 82° (Angles on a straight line)
∠SRN = ∠RSN = 82° (Isosceles triangle)
∠t
= ∠SRN
= 82° (Corresponding angles, PQ//NR)
(b)
∠v
= 180° - 82° - 82°
= 16° (Isosceles triangle NRS)
Answer(s): (a) 82°; (b) 16°