The figure is not drawn to scale. It shows a parallelogram QRST and an isosceles triangle MQT next to it. ∠PTM = 9°. PN and ML are straight lines. Find
- ∠w
- ∠u + ∠v
- ∠v
(a)
∠w
= 180° - ∠PTM
= 180° - 9°
= 171° (Angles on a straight line)
(b)
∠u = ∠QTS (Parallelogram)
∠u + ∠v
= 180° - 9° - 58°
= 113° (Angles on a straight line)
(c)
∠MQT = ∠u (Corresponding angles)
∠MQT = ∠TMQ (Isosceles triangle)
∠u
= 180° - (∠u + ∠v)
= 180° - 113°
= 67°
∠v
= 180° - ∠u - ∠u
= 180° - 67° - 67°
= 46° (Angles sum of triangle)
Answer(s): (a) 171°; (b) 113°; (c) 46°
