The figure is not drawn to scale. It shows a parallelogram KLMN and an isosceles triangle GKN next to it. ∠JNG = 8°. JH and GF are straight lines. Find
- ∠r
- ∠p + ∠q
- ∠q
(a)
∠r
= 180° - ∠JNG
= 180° - 8°
= 172° (Angles on a straight line)
(b)
∠p = ∠KNM (Parallelogram)
∠p + ∠q
= 180° - 8° - 55°
= 117° (Angles on a straight line)
(c)
∠GKN = ∠p (Corresponding angles)
∠GKN = ∠NGK (Isosceles triangle)
∠p
= 180° - (∠p + ∠q)
= 180° - 117°
= 63°
∠q
= 180° - ∠p - ∠p
= 180° - 63° - 63°
= 54° (Angles sum of triangle)
Answer(s): (a) 172°; (b) 117°; (c) 54°