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  • In Fig. 6.10, ∠1 = 60° and ∠6 = 120°. Show that the lines m and n are parallel.

\text{In Fig. 6.10,}\ \angle 1 = 60^{\circ} \text{ and} \angle 6 = 120^{\circ}. Show that the lines m and n are parallel.

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Solution.

Given: The figure \angle 1 = 60^{\circ} and \angle 6 = 120^{\circ}
To show : m \parallel n
Proof: \angle 1 = 60^{\circ}  and \angle 6 = 120^{\circ}
Here, \angle 1 = 60^{\circ} and \angle 6 = 120^{\circ}
Here \angle 1 = \angle 3 (Vertically opposite angles)
\angle 3 = \angle 1 = 60^{\circ}
Now, \angle 3 + \angle 6 = 60^{\circ}+ 120^{\circ}
\angle 3 + \angle 6 = 180^{\circ}
We know if the sum of two interior angles on the same side is 180^{\circ} then the lines are parallel

Hence proved, m \parallel n.

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