In the figure, JKLM is a parallelogram. LP, PQ and JK are straight lines. JMN is an isosceles triangle.
- Find ∠p.
- Find ∠q.
(a)
∠LPJ = ∠KJQ = 66° (Corresponding angles, JK//PL)
∠PNJ
= 180° - ∠LPJ - ∠PJN
= 180° - 66° - 15°
= 99° (Angles sum of triangle)
∠MNJ
= 180° - 99°
= 81° (Angles on a straight line)
∠NMJ = ∠MNJ = 81° (Isosceles triangle)
∠p
= ∠NMJ
= 81° (Corresponding angles, KL//JM)
(b)
∠q
= 180° - 81° - 81°
= 18° (Isosceles triangle JMN)
Answer(s): (a) 81°; (b) 18°