In the figure, LMNP is a parallelogram. NR, RS and LM are straight lines. LPQ is an isosceles triangle.
- Find ∠x.
- Find ∠y.
(a)
∠NRL = ∠MLS = 59° (Corresponding angles, LM//RN)
∠RQL
= 180° - ∠NRL - ∠RLQ
= 180° - 59° - 19°
= 102° (Angles sum of triangle)
∠PQL
= 180° - 102°
= 78° (Angles on a straight line)
∠QPL = ∠PQL = 78° (Isosceles triangle)
∠x
= ∠QPL
= 78° (Corresponding angles, MN//LP)
(b)
∠y
= 180° - 78° - 78°
= 24° (Isosceles triangle LPQ)
Answer(s): (a) 78°; (b) 24°