The figure is not drawn to scale. KLNP is a parallelogram. ∠PKO is 54° and ∠NLM is 32°. KLM is an isosceles triangle and KL = LM.
- Find ∠OML.
- Find ∠KPN.
(a)
∠LOK = 54° (Alternate angles, KP//LN)
∠LOM
= 180° - 54°
= 126° (Angles on a straight line)
∠OML
= 180° - 126° - 32°
= 22° (Angles sum of triangle)
(b)
∠LKO = 22° (Isosceles triangle KLM)
∠KPN
= 180° - 54° - 22°
= 104° (Interior angles, KL//PN)
Answer(s): (a) 22°; (b) 104°