The figure is not drawn to scale. It shows a parallelogram LMNP and an isosceles triangle HLP next to it. ∠KPH = 8°. KJ and HG are straight lines. Find
- ∠s
- ∠q + ∠r
- ∠r
(a)
∠s
= 180° - ∠KPH
= 180° - 8°
= 172° (Angles on a straight line)
(b)
∠q = ∠LPN (Parallelogram)
∠q + ∠r
= 180° - 8° - 55°
= 117° (Angles on a straight line)
(c)
∠HLP = ∠q (Corresponding angles)
∠HLP = ∠PHL (Isosceles triangle)
∠q
= 180° - (∠q + ∠r)
= 180° - 117°
= 63°
∠r
= 180° - ∠q - ∠q
= 180° - 63° - 63°
= 54° (Angles sum of triangle)
Answer(s): (a) 172°; (b) 117°; (c) 54°