In the figure, GHJK is a parallelogram. JM, MN and GH are straight lines. GKL is an isosceles triangle.
- Find ∠a.
- Find ∠b.
(a)
∠JMG = ∠HGN = 59° (Corresponding angles, GH//MJ)
∠MLG
= 180° - ∠JMG - ∠MGL
= 180° - 59° - 19°
= 102° (Angles sum of triangle)
∠KLG
= 180° - 102°
= 78° (Angles on a straight line)
∠LKG = ∠KLG = 78° (Isosceles triangle)
∠a
= ∠LKG
= 78° (Corresponding angles, HJ//GK)
(b)
∠b
= 180° - 78° - 78°
= 24° (Isosceles triangle GKL)
Answer(s): (a) 78°; (b) 24°