In the figure, LMNP is a parallelogram. NR, RS and LM are straight lines. LPQ is an isosceles triangle.
- Find ∠i.
- Find ∠j.
(a)
∠NRL = ∠MLS = 62° (Corresponding angles, LM//RN)
∠RQL
= 180° - ∠NRL - ∠RLQ
= 180° - 62° - 15°
= 103° (Angles sum of triangle)
∠PQL
= 180° - 103°
= 77° (Angles on a straight line)
∠QPL = ∠PQL = 77° (Isosceles triangle)
∠i
= ∠QPL
= 77° (Corresponding angles, MN//LP)
(b)
∠j
= 180° - 77° - 77°
= 26° (Isosceles triangle LPQ)
Answer(s): (a) 77°; (b) 26°