KLMN is a quadrilateral and OKNM is a trapezium in which OK // NM and ∠LKN = 113°, ∠KNM = 122°, ∠LMN = 64° and NM = NK. Find
- ∠KLO
- ∠NKO
- ∠KMN.
(a)
∠KLO
= 360° - 122° -113° - 64°
= 61° (Sum of angles in a quadrilateral)
(b)
∠NKO
= 180° - 122°
= 58° (Interior angles, KO//NC)
(c)
∠KMN
= (180° - 122°) ÷ 2
= 58 ÷ 2
= 29° (Isosceles triangle)
Answer(s): (a) 61°; (b) 58°; (c) 29°