In the figure, LMNP is a parallelogram. NR, RS and LM are straight lines. LPQ is an isosceles triangle.
- Find ∠c.
- Find ∠d.
(a)
∠NRL = ∠MLS = 63° (Corresponding angles, LM//RN)
∠RQL
= 180° - ∠NRL - ∠RLQ
= 180° - 63° - 21°
= 96° (Angles sum of triangle)
∠PQL
= 180° - 96°
= 84° (Angles on a straight line)
∠QPL = ∠PQL = 84° (Isosceles triangle)
∠c
= ∠QPL
= 84° (Corresponding angles, MN//LP)
(b)
∠d
= 180° - 84° - 84°
= 12° (Isosceles triangle LPQ)
Answer(s): (a) 84°; (b) 12°