In the figure, KLMN is a parallelogram. MQ, QR and KL are straight lines. KNP is an isosceles triangle.
- Find ∠w.
- Find ∠x.
(a)
∠MQK = ∠LKR = 59° (Corresponding angles, KL//QM)
∠QPK
= 180° - ∠MQK - ∠QKP
= 180° - 59° - 20°
= 101° (Angles sum of triangle)
∠NPK
= 180° - 101°
= 79° (Angles on a straight line)
∠PNK = ∠NPK = 79° (Isosceles triangle)
∠w
= ∠PNK
= 79° (Corresponding angles, LM//KN)
(b)
∠x
= 180° - 79° - 79°
= 22° (Isosceles triangle KNP)
Answer(s): (a) 79°; (b) 22°