The figure is not drawn to scale. KLNP is a parallelogram. ∠PKO is 56° and ∠NLM is 29°. KLM is an isosceles triangle and KL = LM.
- Find ∠OML.
- Find ∠KPN.
(a)
∠LOK = 56° (Alternate angles, KP//LN)
∠LOM
= 180° - 56°
= 124° (Angles on a straight line)
∠OML
= 180° - 124° - 29°
= 27° (Angles sum of triangle)
(b)
∠LKO = 27° (Isosceles triangle KLM)
∠KPN
= 180° - 56° - 27°
= 97° (Interior angles, KL//PN)
Answer(s): (a) 27°; (b) 97°