In the figure, MNPQ is a parallelogram. O is the centre of the circle. Find
- ∠MQP
- ∠MNQ
(a)
∠ONQ = ∠NQO = 44° (Angle properties within a circle)
∠QON
= 180° - 44° - 44°
= 92° (Angles sum of triangle)
∠OMN + ∠ONM = ∠NOQ (Exterior angle of a triangle)
∠OMN = ∠ONM (Isosceles triangle, OM = ON)
∠OMN
= 92° ÷ 2
= 46° (Exterior angle of a triangle)
∠MQP
= 180° - 46°
= 134° (Interior angles)
(b)
∠MNQ
= 180° - 46° - 44°
= 90° (Angle sum of triangles)
Answer(s): (a) 134°; (b) 90°