In the figure, KLMN is a parallelogram. MQ, QR and KL are straight lines. KNP is an isosceles triangle.
- Find ∠r.
- Find ∠s.
(a)
∠MQK = ∠LKR = 59° (Corresponding angles, KL//QM)
∠QPK
= 180° - ∠MQK - ∠QKP
= 180° - 59° - 18°
= 103° (Angles sum of triangle)
∠NPK
= 180° - 103°
= 77° (Angles on a straight line)
∠PNK = ∠NPK = 77° (Isosceles triangle)
∠r
= ∠PNK
= 77° (Corresponding angles, LM//KN)
(b)
∠s
= 180° - 77° - 77°
= 26° (Isosceles triangle KNP)
Answer(s): (a) 77°; (b) 26°
