In the figure, NPQR is a parallelogram. QT, TU and NP are straight lines. NRS is an isosceles triangle.
- Find ∠a.
- Find ∠b.
(a)
∠QTN = ∠PNU = 58° (Corresponding angles, NP//TQ)
∠TSN
= 180° - ∠QTN - ∠TNS
= 180° - 58° - 17°
= 105° (Angles sum of triangle)
∠RSN
= 180° - 105°
= 75° (Angles on a straight line)
∠SRN = ∠RSN = 75° (Isosceles triangle)
∠a
= ∠SRN
= 75° (Corresponding angles, PQ//NR)
(b)
∠b
= 180° - 75° - 75°
= 30° (Isosceles triangle NRS)
Answer(s): (a) 75°; (b) 30°