The figure is not drawn to scale. It shows a parallelogram RSTU and an isosceles triangle NRU next to it. ∠QUN = 13°. QP and NM are straight lines. Find
- ∠x
- ∠v + ∠w
- ∠w
(a)
∠x
= 180° - ∠QUN
= 180° - 13°
= 167° (Angles on a straight line)
(b)
∠v = ∠RUT (Parallelogram)
∠v + ∠w
= 180° - 13° - 55°
= 112° (Angles on a straight line)
(c)
∠NRU = ∠v (Corresponding angles)
∠NRU = ∠UNR (Isosceles triangle)
∠v
= 180° - (∠v + ∠w)
= 180° - 112°
= 68°
∠w
= 180° - ∠v - ∠v
= 180° - 68° - 68°
= 44° (Angles sum of triangle)
Answer(s): (a) 167°; (b) 112°; (c) 44°