The figure is not drawn to scale. It shows a parallelogram PQRS and an isosceles triangle LPS next to it. ∠NSL = 9°. NM and LK are straight lines. Find
- ∠v
- ∠t + ∠u
- ∠u
(a)
∠v
= 180° - ∠NSL
= 180° - 9°
= 171° (Angles on a straight line)
(b)
∠t = ∠PSR (Parallelogram)
∠t + ∠u
= 180° - 9° - 56°
= 115° (Angles on a straight line)
(c)
∠LPS = ∠t (Corresponding angles)
∠LPS = ∠SLP (Isosceles triangle)
∠t
= 180° - (∠t + ∠u)
= 180° - 115°
= 65°
∠u
= 180° - ∠t - ∠t
= 180° - 65° - 65°
= 50° (Angles sum of triangle)
Answer(s): (a) 171°; (b) 115°; (c) 50°