In the figure, KLMN is a parallelogram. O is the centre of the circle. Find
- ∠KNM
- ∠KLN
(a)
∠OLN = ∠LNO = 37° (Angle properties within a circle)
∠NOL
= 180° - 37° - 37°
= 106° (Angles sum of triangle)
∠OKL + ∠OLK = ∠LON (Exterior angle of a triangle)
∠OKL = ∠OLK (Isosceles triangle, OK = OL)
∠OKL
= 106° ÷ 2
= 53° (Exterior angle of a triangle)
∠KNM
= 180° - 53°
= 127° (Interior angles)
(b)
∠KLN
= 180° - 53° - 37°
= 90° (Angle sum of triangles)
Answer(s): (a) 127°; (b) 90°