In the figure, NPQR is a parallelogram. QT, TU and NP are straight lines. NRS is an isosceles triangle.
- Find ∠b.
- Find ∠c.
(a)
∠QTN = ∠PNU = 59° (Corresponding angles, NP//TQ)
∠TSN
= 180° - ∠QTN - ∠TNS
= 180° - 59° - 19°
= 102° (Angles sum of triangle)
∠RSN
= 180° - 102°
= 78° (Angles on a straight line)
∠SRN = ∠RSN = 78° (Isosceles triangle)
∠b
= ∠SRN
= 78° (Corresponding angles, PQ//NR)
(b)
∠c
= 180° - 78° - 78°
= 24° (Isosceles triangle NRS)
Answer(s): (a) 78°; (b) 24°