In the figure, FGHJ is a parallelogram. HL, LM and FG are straight lines. FJK is an isosceles triangle.
- Find ∠r.
- Find ∠s.
(a)
∠HLF = ∠GFM = 58° (Corresponding angles, FG//LH)
∠LKF
= 180° - ∠HLF - ∠LFK
= 180° - 58° - 19°
= 103° (Angles sum of triangle)
∠JKF
= 180° - 103°
= 77° (Angles on a straight line)
∠KJF = ∠JKF = 77° (Isosceles triangle)
∠r
= ∠KJF
= 77° (Corresponding angles, GH//FJ)
(b)
∠s
= 180° - 77° - 77°
= 26° (Isosceles triangle FJK)
Answer(s): (a) 77°; (b) 26°