The figure is not drawn to scale. It shows a parallelogram RSTU and an isosceles triangle NRU next to it. ∠QUN = 9°. QP and NM are straight lines. Find
- ∠x
- ∠v + ∠w
- ∠w
(a)
∠x
= 180° - ∠QUN
= 180° - 9°
= 171° (Angles on a straight line)
(b)
∠v = ∠RUT (Parallelogram)
∠v + ∠w
= 180° - 9° - 57°
= 114° (Angles on a straight line)
(c)
∠NRU = ∠v (Corresponding angles)
∠NRU = ∠UNR (Isosceles triangle)
∠v
= 180° - (∠v + ∠w)
= 180° - 114°
= 66°
∠w
= 180° - ∠v - ∠v
= 180° - 66° - 66°
= 48° (Angles sum of triangle)
Answer(s): (a) 171°; (b) 114°; (c) 48°