In the figure, FGHJ is a parallelogram. HL, LM and FG are straight lines. FJK is an isosceles triangle.
- Find ∠q.
- Find ∠r.
(a)
∠HLF = ∠GFM = 65° (Corresponding angles, FG//LH)
∠LKF
= 180° - ∠HLF - ∠LFK
= 180° - 65° - 17°
= 98° (Angles sum of triangle)
∠JKF
= 180° - 98°
= 82° (Angles on a straight line)
∠KJF = ∠JKF = 82° (Isosceles triangle)
∠q
= ∠KJF
= 82° (Corresponding angles, GH//FJ)
(b)
∠r
= 180° - 82° - 82°
= 16° (Isosceles triangle FJK)
Answer(s): (a) 82°; (b) 16°
