In the figure, KLMN is a parallelogram. O is the centre of the circle. Find
- ∠KNM
- ∠KLN
(a)
∠OLN = ∠LNO = 25° (Angle properties within a circle)
∠NOL
= 180° - 25° - 25°
= 130° (Angles sum of triangle)
∠OKL + ∠OLK = ∠LON (Exterior angle of a triangle)
∠OKL = ∠OLK (Isosceles triangle, OK = OL)
∠OKL
= 130° ÷ 2
= 65° (Exterior angle of a triangle)
∠KNM
= 180° - 65°
= 115° (Interior angles)
(b)
∠KLN
= 180° - 65° - 25°
= 90° (Angle sum of triangles)
Answer(s): (a) 115°; (b) 90°