In the figure, FGHJ is a parallelogram. HL, LM and FG are straight lines. FJK is an isosceles triangle.
- Find ∠m.
- Find ∠n.
(a)
∠HLF = ∠GFM = 59° (Corresponding angles, FG//LH)
∠LKF
= 180° - ∠HLF - ∠LFK
= 180° - 59° - 21°
= 100° (Angles sum of triangle)
∠JKF
= 180° - 100°
= 80° (Angles on a straight line)
∠KJF = ∠JKF = 80° (Isosceles triangle)
∠m
= ∠KJF
= 80° (Corresponding angles, GH//FJ)
(b)
∠n
= 180° - 80° - 80°
= 20° (Isosceles triangle FJK)
Answer(s): (a) 80°; (b) 20°