The figure is not drawn to scale. It shows a parallelogram STUV and an isosceles triangle PSV next to it. ∠RVP = 12°. RQ and PN are straight lines. Find
- ∠y
- ∠w + ∠x
- ∠x
(a)
∠y
= 180° - ∠RVP
= 180° - 12°
= 168° (Angles on a straight line)
(b)
∠w = ∠SVU (Parallelogram)
∠w + ∠x
= 180° - 12° - 51°
= 117° (Angles on a straight line)
(c)
∠PSV = ∠w (Corresponding angles)
∠PSV = ∠VPS (Isosceles triangle)
∠w
= 180° - (∠w + ∠x)
= 180° - 117°
= 63°
∠x
= 180° - ∠w - ∠w
= 180° - 63° - 63°
= 54° (Angles sum of triangle)
Answer(s): (a) 168°; (b) 117°; (c) 54°