In the figure, LMNP is a parallelogram. O is the centre of the circle. Find
- ∠LPN
- ∠LMP
(a)
∠OMP = ∠MPO = 37° (Angle properties within a circle)
∠POM
= 180° - 37° - 37°
= 106° (Angles sum of triangle)
∠OLM + ∠OML = ∠MOP (Exterior angle of a triangle)
∠OLM = ∠OML (Isosceles triangle, OL = OM)
∠OLM
= 106° ÷ 2
= 53° (Exterior angle of a triangle)
∠LPN
= 180° - 53°
= 127° (Interior angles)
(b)
∠LMP
= 180° - 53° - 37°
= 90° (Angle sum of triangles)
Answer(s): (a) 127°; (b) 90°