Question

Question 2
In the figure, $\angle 1={60}^{\circ }and\angle 6={120}^{\circ }$. Show that the lines m and n are parallel.

Answer 1

Given in the figure $\angle 1={60}^{\circ }and\angle 6={120}^{\circ }$
To show: m ∥ n
Proof:
$\angle 1={60}^{\circ }and\angle 6={120}^{\circ }$
$\angle 1=\angle 3$ (Vertically opposite angles)
$\therefore \angle 3=\angle 1={60}^{\circ }$
$Now,\angle 3+\angle 6={60}^{\circ }+{120}^{\circ }$
$\Rightarrow \angle 3+\angle 6={180}^{\circ }$
We know that, if the sum of two interior angles on same side of a transversal is ${180}^{\circ }$, then lines are parallel.
Hence, m ∥ n.