Question

Look at the following figure and fill in the blanks :

In the figure, $l$ and $m$ are the parallel lines and $p$is a transversal.

If $\angle 1=150°$, then $\angle 3=$………

Answer 1

Vertically opposite angles :

When two lines intersect, the opposite angles are equal. These angles are called vertically opposite angles because they are opposite each other at a vertex. As given in the figure :

Here $\angle 1,\angle 3$ and $\angle 2,\angle 4$are the two pairs of vertically opposite angles that are equal to each other.

Similarly, as per the question :

$\angle 1$ and $\angle 3$ are opposite to each other.

So, angles $\angle 1$ and $\angle 3$ are vertically opposite angles.

$\angle 1=\angle 3$ ($\because$Vertically opposite angles are equal)

$\angle 3=150°$ ($\because$ $\angle 1=\angle 3$ and as given $\angle 1=150°$)

Hence, the measure of $\angle 3$ is $150°$, i.e. $\angle 3=150°$.