The figure is not drawn to scale. It shows a parallelogram RSTU and an isosceles triangle NRU next to it. ∠QUN = 10°. QP and NM are straight lines. Find
- ∠x
- ∠v + ∠w
- ∠w
(a)
∠x
= 180° - ∠QUN
= 180° - 10°
= 170° (Angles on a straight line)
(b)
∠v = ∠RUT (Parallelogram)
∠v + ∠w
= 180° - 10° - 52°
= 118° (Angles on a straight line)
(c)
∠NRU = ∠v (Corresponding angles)
∠NRU = ∠UNR (Isosceles triangle)
∠v
= 180° - (∠v + ∠w)
= 180° - 118°
= 62°
∠w
= 180° - ∠v - ∠v
= 180° - 62° - 62°
= 56° (Angles sum of triangle)
Answer(s): (a) 170°; (b) 118°; (c) 56°