KLMN is a quadrilateral and OKNM is a trapezium in which OK // NM and ∠LKN = 108°, ∠KNM = 128°, ∠LMN = 67° and NM = NK. Find
- ∠KLO
- ∠NKO
- ∠KMN.
(a)
∠KLO
= 360° - 128° -108° - 67°
= 57° (Sum of angles in a quadrilateral)
(b)
∠NKO
= 180° - 128°
= 52° (Interior angles, KO//NC)
(c)
∠KMN
= (180° - 128°) ÷ 2
= 52 ÷ 2
= 26° (Isosceles triangle)
Answer(s): (a) 57°; (b) 52°; (c) 26°