In the figure, NPQR is a parallelogram. QT, TU and NP are straight lines. NRS is an isosceles triangle.
- Find ∠h.
- Find ∠i.
(a)
∠QTN = ∠PNU = 61° (Corresponding angles, NP//TQ)
∠TSN
= 180° - ∠QTN - ∠TNS
= 180° - 61° - 16°
= 103° (Angles sum of triangle)
∠RSN
= 180° - 103°
= 77° (Angles on a straight line)
∠SRN = ∠RSN = 77° (Isosceles triangle)
∠h
= ∠SRN
= 77° (Corresponding angles, PQ//NR)
(b)
∠i
= 180° - 77° - 77°
= 26° (Isosceles triangle NRS)
Answer(s): (a) 77°; (b) 26°