Question

In the figure, transversal l, intersects two lines m and n, $\angle 4={110}^{0}and\angle 7={65}^0$. Is m||n?

Answer 1

A transversal l, intersects two lines m and n, forming $\angle 1,\angle 2,\angle 3,\angle 4,\angle 5,\angle 6,\angle 7and\angle 8$
$\angle 4={110}^0,and\angle 7={65}^0$
To prove: Whether m||n or not
Proof: $\angle 4={110}^{0}and\angle 7={65}^0$
$\angle 7=\angle 5$ (Vertically opposite angles)
$\therefore \angle 5={65}^0$
Now $\angle 4+\angle 5={110}^0+{65}^0={175}^0$
$\therefore$ Sum of co-interior angles $\angle 4and\angle 5$ is not ${180}^0$.
$\therefore$ m is not parallel to n