The figure is not drawn to scale. It shows a parallelogram PQRS and an isosceles triangle LPS next to it. ∠NSL = 13°. NM and LK are straight lines. Find
- ∠v
- ∠t + ∠u
- ∠u
(a)
∠v
= 180° - ∠NSL
= 180° - 13°
= 167° (Angles on a straight line)
(b)
∠t = ∠PSR (Parallelogram)
∠t + ∠u
= 180° - 13° - 54°
= 113° (Angles on a straight line)
(c)
∠LPS = ∠t (Corresponding angles)
∠LPS = ∠SLP (Isosceles triangle)
∠t
= 180° - (∠t + ∠u)
= 180° - 113°
= 67°
∠u
= 180° - ∠t - ∠t
= 180° - 67° - 67°
= 46° (Angles sum of triangle)
Answer(s): (a) 167°; (b) 113°; (c) 46°
