In the figure, KLMN is a parallelogram. MQ, QR and KL are straight lines. KNP is an isosceles triangle.
- Find ∠x.
- Find ∠y.
(a)
∠MQK = ∠LKR = 65° (Corresponding angles, KL//QM)
∠QPK
= 180° - ∠MQK - ∠QKP
= 180° - 65° - 21°
= 94° (Angles sum of triangle)
∠NPK
= 180° - 94°
= 86° (Angles on a straight line)
∠PNK = ∠NPK = 86° (Isosceles triangle)
∠x
= ∠PNK
= 86° (Corresponding angles, LM//KN)
(b)
∠y
= 180° - 86° - 86°
= 8° (Isosceles triangle KNP)
Answer(s): (a) 86°; (b) 8°