The figure is not drawn to scale. It shows a parallelogram RSTU and an isosceles triangle NRU next to it. ∠QUN = 14°. QP and NM are straight lines. Find
- ∠x
- ∠v + ∠w
- ∠w
(a)
∠x
= 180° - ∠QUN
= 180° - 14°
= 166° (Angles on a straight line)
(b)
∠v = ∠RUT (Parallelogram)
∠v + ∠w
= 180° - 14° - 56°
= 110° (Angles on a straight line)
(c)
∠NRU = ∠v (Corresponding angles)
∠NRU = ∠UNR (Isosceles triangle)
∠v
= 180° - (∠v + ∠w)
= 180° - 110°
= 70°
∠w
= 180° - ∠v - ∠v
= 180° - 70° - 70°
= 40° (Angles sum of triangle)
Answer(s): (a) 166°; (b) 110°; (c) 40°
