In the figure, GHJK is a parallelogram. JM, MN and GH are straight lines. GKL is an isosceles triangle.
- Find ∠q.
- Find ∠r.
(a)
∠JMG = ∠HGN = 65° (Corresponding angles, GH//MJ)
∠MLG
= 180° - ∠JMG - ∠MGL
= 180° - 65° - 21°
= 94° (Angles sum of triangle)
∠KLG
= 180° - 94°
= 86° (Angles on a straight line)
∠LKG = ∠KLG = 86° (Isosceles triangle)
∠q
= ∠LKG
= 86° (Corresponding angles, HJ//GK)
(b)
∠r
= 180° - 86° - 86°
= 8° (Isosceles triangle GKL)
Answer(s): (a) 86°; (b) 8°