In the figure, LMNP is a parallelogram. O is the centre of the circle. Find
- ∠LPN
- ∠LMP
(a)
∠OMP = ∠MPO = 45° (Angle properties within a circle)
∠POM
= 180° - 45° - 45°
= 90° (Angles sum of triangle)
∠OLM + ∠OML = ∠MOP (Exterior angle of a triangle)
∠OLM = ∠OML (Isosceles triangle, OL = OM)
∠OLM
= 90° ÷ 2
= 45° (Exterior angle of a triangle)
∠LPN
= 180° - 45°
= 135° (Interior angles)
(b)
∠LMP
= 180° - 45° - 45°
= 90° (Angle sum of triangles)
Answer(s): (a) 135°; (b) 90°