The figure is not drawn to scale. It shows a parallelogram TUVW and an isosceles triangle QTW next to it. ∠SWQ = 14°. SR and QP are straight lines. Find
- ∠z
- ∠x + ∠y
- ∠y
(a)
∠z
= 180° - ∠SWQ
= 180° - 14°
= 166° (Angles on a straight line)
(b)
∠x = ∠TWV (Parallelogram)
∠x + ∠y
= 180° - 14° - 56°
= 110° (Angles on a straight line)
(c)
∠QTW = ∠x (Corresponding angles)
∠QTW = ∠WQT (Isosceles triangle)
∠x
= 180° - (∠x + ∠y)
= 180° - 110°
= 70°
∠y
= 180° - ∠x - ∠x
= 180° - 70° - 70°
= 40° (Angles sum of triangle)
Answer(s): (a) 166°; (b) 110°; (c) 40°