The figure is not drawn to scale. It shows a parallelogram JKLM and an isosceles triangle FJM next to it. ∠HMF = 12°. HG and FE are straight lines. Find
- ∠q
- ∠n + ∠p
- ∠p
(a)
∠q
= 180° - ∠HMF
= 180° - 12°
= 168° (Angles on a straight line)
(b)
∠n = ∠JML (Parallelogram)
∠n + ∠p
= 180° - 12° - 57°
= 111° (Angles on a straight line)
(c)
∠FJM = ∠n (Corresponding angles)
∠FJM = ∠MFJ (Isosceles triangle)
∠n
= 180° - (∠n + ∠p)
= 180° - 111°
= 69°
∠p
= 180° - ∠n - ∠n
= 180° - 69° - 69°
= 42° (Angles sum of triangle)
Answer(s): (a) 168°; (b) 111°; (c) 42°