The figure is not drawn to scale. It shows a parallelogram TUVW and an isosceles triangle QTW next to it. ∠SWQ = 10°. SR and QP are straight lines. Find
- ∠z
- ∠x + ∠y
- ∠y
(a)
∠z
= 180° - ∠SWQ
= 180° - 10°
= 170° (Angles on a straight line)
(b)
∠x = ∠TWV (Parallelogram)
∠x + ∠y
= 180° - 10° - 51°
= 119° (Angles on a straight line)
(c)
∠QTW = ∠x (Corresponding angles)
∠QTW = ∠WQT (Isosceles triangle)
∠x
= 180° - (∠x + ∠y)
= 180° - 119°
= 61°
∠y
= 180° - ∠x - ∠x
= 180° - 61° - 61°
= 58° (Angles sum of triangle)
Answer(s): (a) 170°; (b) 119°; (c) 58°
