In the figure, GHJK is a parallelogram. JM, MN and GH are straight lines. GKL is an isosceles triangle.
- Find ∠w.
- Find ∠x.
(a)
∠JMG = ∠HGN = 58° (Corresponding angles, GH//MJ)
∠MLG
= 180° - ∠JMG - ∠MGL
= 180° - 58° - 16°
= 106° (Angles sum of triangle)
∠KLG
= 180° - 106°
= 74° (Angles on a straight line)
∠LKG = ∠KLG = 74° (Isosceles triangle)
∠w
= ∠LKG
= 74° (Corresponding angles, HJ//GK)
(b)
∠x
= 180° - 74° - 74°
= 32° (Isosceles triangle GKL)
Answer(s): (a) 74°; (b) 32°