In the figure, LMNP is a parallelogram. NR, RS and LM are straight lines. LPQ is an isosceles triangle.
- Find ∠n.
- Find ∠p.
(a)
∠NRL = ∠MLS = 64° (Corresponding angles, LM//RN)
∠RQL
= 180° - ∠NRL - ∠RLQ
= 180° - 64° - 15°
= 101° (Angles sum of triangle)
∠PQL
= 180° - 101°
= 79° (Angles on a straight line)
∠QPL = ∠PQL = 79° (Isosceles triangle)
∠n
= ∠QPL
= 79° (Corresponding angles, MN//LP)
(b)
∠p
= 180° - 79° - 79°
= 22° (Isosceles triangle LPQ)
Answer(s): (a) 79°; (b) 22°
