In the figure, JKLM is a parallelogram. LP, PQ and JK are straight lines. JMN is an isosceles triangle.
- Find ∠i.
- Find ∠j.
(a)
∠LPJ = ∠KJQ = 58° (Corresponding angles, JK//PL)
∠PNJ
= 180° - ∠LPJ - ∠PJN
= 180° - 58° - 18°
= 104° (Angles sum of triangle)
∠MNJ
= 180° - 104°
= 76° (Angles on a straight line)
∠NMJ = ∠MNJ = 76° (Isosceles triangle)
∠i
= ∠NMJ
= 76° (Corresponding angles, KL//JM)
(b)
∠j
= 180° - 76° - 76°
= 28° (Isosceles triangle JMN)
Answer(s): (a) 76°; (b) 28°