The figure is not drawn to scale. It shows a parallelogram MNPQ and an isosceles triangle JMQ next to it. ∠LQJ = 8°. LK and JH are straight lines. Find
- ∠t
- ∠r + ∠s
- ∠s
(a)
∠t
= 180° - ∠LQJ
= 180° - 8°
= 172° (Angles on a straight line)
(b)
∠r = ∠MQP (Parallelogram)
∠r + ∠s
= 180° - 8° - 63°
= 109° (Angles on a straight line)
(c)
∠JMQ = ∠r (Corresponding angles)
∠JMQ = ∠QJM (Isosceles triangle)
∠r
= 180° - (∠r + ∠s)
= 180° - 109°
= 71°
∠s
= 180° - ∠r - ∠r
= 180° - 71° - 71°
= 38° (Angles sum of triangle)
Answer(s): (a) 172°; (b) 109°; (c) 38°
