The figure is not drawn to scale. It shows a parallelogram MNPQ and an isosceles triangle JMQ next to it. ∠LQJ = 9°. LK and JH are straight lines. Find
- ∠t
- ∠r + ∠s
- ∠s
(a)
∠t
= 180° - ∠LQJ
= 180° - 9°
= 171° (Angles on a straight line)
(b)
∠r = ∠MQP (Parallelogram)
∠r + ∠s
= 180° - 9° - 52°
= 119° (Angles on a straight line)
(c)
∠JMQ = ∠r (Corresponding angles)
∠JMQ = ∠QJM (Isosceles triangle)
∠r
= 180° - (∠r + ∠s)
= 180° - 119°
= 61°
∠s
= 180° - ∠r - ∠r
= 180° - 61° - 61°
= 58° (Angles sum of triangle)
Answer(s): (a) 171°; (b) 119°; (c) 58°