In the figure, KLMN is a parallelogram. MQ, QR and KL are straight lines. KNP is an isosceles triangle.
- Find ∠f.
- Find ∠g.
(a)
∠MQK = ∠LKR = 64° (Corresponding angles, KL//QM)
∠QPK
= 180° - ∠MQK - ∠QKP
= 180° - 64° - 19°
= 97° (Angles sum of triangle)
∠NPK
= 180° - 97°
= 83° (Angles on a straight line)
∠PNK = ∠NPK = 83° (Isosceles triangle)
∠f
= ∠PNK
= 83° (Corresponding angles, LM//KN)
(b)
∠g
= 180° - 83° - 83°
= 14° (Isosceles triangle KNP)
Answer(s): (a) 83°; (b) 14°