In the figure, LMNP is a parallelogram. NR, RS and LM are straight lines. LPQ is an isosceles triangle.
- Find ∠k.
- Find ∠m.
(a)
∠NRL = ∠MLS = 58° (Corresponding angles, LM//RN)
∠RQL
= 180° - ∠NRL - ∠RLQ
= 180° - 58° - 18°
= 104° (Angles sum of triangle)
∠PQL
= 180° - 104°
= 76° (Angles on a straight line)
∠QPL = ∠PQL = 76° (Isosceles triangle)
∠k
= ∠QPL
= 76° (Corresponding angles, MN//LP)
(b)
∠m
= 180° - 76° - 76°
= 28° (Isosceles triangle LPQ)
Answer(s): (a) 76°; (b) 28°