In the figure, NPQR is a parallelogram. QT, TU and NP are straight lines. NRS is an isosceles triangle.
- Find ∠v.
- Find ∠w.
(a)
∠QTN = ∠PNU = 58° (Corresponding angles, NP//TQ)
∠TSN
= 180° - ∠QTN - ∠TNS
= 180° - 58° - 15°
= 107° (Angles sum of triangle)
∠RSN
= 180° - 107°
= 73° (Angles on a straight line)
∠SRN = ∠RSN = 73° (Isosceles triangle)
∠v
= ∠SRN
= 73° (Corresponding angles, PQ//NR)
(b)
∠w
= 180° - 73° - 73°
= 34° (Isosceles triangle NRS)
Answer(s): (a) 73°; (b) 34°