Q.6 In the given figure below, decide whether l is parallel to m.

(i) Sum of interior angles on the same side of transversal = 126° + 44° = 170° $$\neq$$180°
$$\therefore$$ l is not parallel to m.

(ii) Let angle opposite to 75° be x.
x = 75° [Vertically opposite angles]
$$\therefore$$ Sum of interior angles on the same side of transversal
= x + 75° = 75° + 75°
= 150° $$\neq$$ 180°
$$\therefore$$ l is not parallel to m.

(iii) Let the angle opposite to 57° be y.
$$\therefore$$ $$\angle$$y = 57° (Vertically opposite angles)
$$\therefore$$ Sum of interior angles on the same side of transversal
= 57° + 123° = 180°
$$\therefore$$ l is parallel to m.

(iv) Let angle opposite to 72° be z.
$$\therefore$$z = 70° (Vertically opposite angle)
[Sum of interior angles on the same side of transversal]
= z + 98° = 72° + 98°= 170° $$\neq$$ 180°
$$\therefore$$ l is not parallel to m.