The figure is not drawn to scale. It shows a parallelogram STUV and an isosceles triangle PSV next to it. ∠RVP = 10°. RQ and PN are straight lines. Find
- ∠y
- ∠w + ∠x
- ∠x
(a)
∠y
= 180° - ∠RVP
= 180° - 10°
= 170° (Angles on a straight line)
(b)
∠w = ∠SVU (Parallelogram)
∠w + ∠x
= 180° - 10° - 57°
= 113° (Angles on a straight line)
(c)
∠PSV = ∠w (Corresponding angles)
∠PSV = ∠VPS (Isosceles triangle)
∠w
= 180° - (∠w + ∠x)
= 180° - 113°
= 67°
∠x
= 180° - ∠w - ∠w
= 180° - 67° - 67°
= 46° (Angles sum of triangle)
Answer(s): (a) 170°; (b) 113°; (c) 46°