In the figure, NPQR is a parallelogram. QT, TU and NP are straight lines. NRS is an isosceles triangle.
- Find ∠p.
- Find ∠q.
(a)
∠QTN = ∠PNU = 59° (Corresponding angles, NP//TQ)
∠TSN
= 180° - ∠QTN - ∠TNS
= 180° - 59° - 20°
= 101° (Angles sum of triangle)
∠RSN
= 180° - 101°
= 79° (Angles on a straight line)
∠SRN = ∠RSN = 79° (Isosceles triangle)
∠p
= ∠SRN
= 79° (Corresponding angles, PQ//NR)
(b)
∠q
= 180° - 79° - 79°
= 22° (Isosceles triangle NRS)
Answer(s): (a) 79°; (b) 22°