Question

In the figure $ \angle 1=60°$ and $ \angle 6=120°$. Show that the lines $ m$ and $ n$ are parallel.

! (21 \3/4/ (6]5) \7/8/ 

Answer 1

Prove that the given lines are parallel

We need to prove the lines $m$ and $n$ are parallel

Given, $\angle 1=60°$ and $\angle 6=120°$

Also, $\angle 1=\angle 3$ since they are vertically opposite angle

$\therefore \angle 1=\angle 3=60°$

Now

$$\begin{gathered} \angle 3+\angle 6=60°+120° \\ \Rightarrow \angle 3+\angle 6=180° \end{gathered}$$

We know that if the sum of two interior angle of same side of the line is $180°$, then the lines are parallel line

Hence proved that the lines $m$ and $n$ are parallel.