In the figure, NPQR is a parallelogram. QT, TU and NP are straight lines. NRS is an isosceles triangle.
- Find ∠j.
- Find ∠k.
(a)
∠QTN = ∠PNU = 61° (Corresponding angles, NP//TQ)
∠TSN
= 180° - ∠QTN - ∠TNS
= 180° - 61° - 20°
= 99° (Angles sum of triangle)
∠RSN
= 180° - 99°
= 81° (Angles on a straight line)
∠SRN = ∠RSN = 81° (Isosceles triangle)
∠j
= ∠SRN
= 81° (Corresponding angles, PQ//NR)
(b)
∠k
= 180° - 81° - 81°
= 18° (Isosceles triangle NRS)
Answer(s): (a) 81°; (b) 18°
