The figure is not drawn to scale. It shows a parallelogram JKLM and an isosceles triangle FJM next to it. ∠HMF = 10°. HG and FE are straight lines. Find
- ∠q
- ∠n + ∠p
- ∠p
(a)
∠q
= 180° - ∠HMF
= 180° - 10°
= 170° (Angles on a straight line)
(b)
∠n = ∠JML (Parallelogram)
∠n + ∠p
= 180° - 10° - 58°
= 112° (Angles on a straight line)
(c)
∠FJM = ∠n (Corresponding angles)
∠FJM = ∠MFJ (Isosceles triangle)
∠n
= 180° - (∠n + ∠p)
= 180° - 112°
= 68°
∠p
= 180° - ∠n - ∠n
= 180° - 68° - 68°
= 44° (Angles sum of triangle)
Answer(s): (a) 170°; (b) 112°; (c) 44°