In the figure, JKLM is a parallelogram. LP, PQ and JK are straight lines. JMN is an isosceles triangle.
- Find ∠f.
- Find ∠g.
(a)
∠LPJ = ∠KJQ = 65° (Corresponding angles, JK//PL)
∠PNJ
= 180° - ∠LPJ - ∠PJN
= 180° - 65° - 18°
= 97° (Angles sum of triangle)
∠MNJ
= 180° - 97°
= 83° (Angles on a straight line)
∠NMJ = ∠MNJ = 83° (Isosceles triangle)
∠f
= ∠NMJ
= 83° (Corresponding angles, KL//JM)
(b)
∠g
= 180° - 83° - 83°
= 14° (Isosceles triangle JMN)
Answer(s): (a) 83°; (b) 14°