The figure is not drawn to scale. KLNP is a parallelogram. ∠PKO is 59° and ∠NLM is 31°. KLM is an isosceles triangle and KL = LM.
- Find ∠OML.
- Find ∠KPN.
(a)
∠LOK = 59° (Alternate angles, KP//LN)
∠LOM
= 180° - 59°
= 121° (Angles on a straight line)
∠OML
= 180° - 121° - 31°
= 28° (Angles sum of triangle)
(b)
∠LKO = 28° (Isosceles triangle KLM)
∠KPN
= 180° - 59° - 28°
= 93° (Interior angles, KL//PN)
Answer(s): (a) 28°; (b) 93°