The figure is not drawn to scale. It shows a parallelogram JKLM and an isosceles triangle FJM next to it. ∠HMF = 9°. HG and FE are straight lines. Find
- ∠q
- ∠n + ∠p
- ∠p
(a)
∠q
= 180° - ∠HMF
= 180° - 9°
= 171° (Angles on a straight line)
(b)
∠n = ∠JML (Parallelogram)
∠n + ∠p
= 180° - 9° - 54°
= 117° (Angles on a straight line)
(c)
∠FJM = ∠n (Corresponding angles)
∠FJM = ∠MFJ (Isosceles triangle)
∠n
= 180° - (∠n + ∠p)
= 180° - 117°
= 63°
∠p
= 180° - ∠n - ∠n
= 180° - 63° - 63°
= 54° (Angles sum of triangle)
Answer(s): (a) 171°; (b) 117°; (c) 54°