In the figure, KLMN is a parallelogram. O is the centre of the circle. Find
- ∠KNM
- ∠KLN
(a)
∠OLN = ∠LNO = 30° (Angle properties within a circle)
∠NOL
= 180° - 30° - 30°
= 120° (Angles sum of triangle)
∠OKL + ∠OLK = ∠LON (Exterior angle of a triangle)
∠OKL = ∠OLK (Isosceles triangle, OK = OL)
∠OKL
= 120° ÷ 2
= 60° (Exterior angle of a triangle)
∠KNM
= 180° - 60°
= 120° (Interior angles)
(b)
∠KLN
= 180° - 60° - 30°
= 90° (Angle sum of triangles)
Answer(s): (a) 120°; (b) 90°