In the figure, KLMN is a parallelogram. MQ, QR and KL are straight lines. KNP is an isosceles triangle.
- Find ∠d.
- Find ∠e.
(a)
∠MQK = ∠LKR = 60° (Corresponding angles, KL//QM)
∠QPK
= 180° - ∠MQK - ∠QKP
= 180° - 60° - 21°
= 99° (Angles sum of triangle)
∠NPK
= 180° - 99°
= 81° (Angles on a straight line)
∠PNK = ∠NPK = 81° (Isosceles triangle)
∠d
= ∠PNK
= 81° (Corresponding angles, LM//KN)
(b)
∠e
= 180° - 81° - 81°
= 18° (Isosceles triangle KNP)
Answer(s): (a) 81°; (b) 18°