Question

Fill in the blanks :

In the figure :

$\angle 6$ and $\angle 7$are equal because they are ……………… angles.

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 to each other at a vertex. As shown in the given figure :

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

Similarly, as per the question :

$\angle 6$ and $\angle 7$ are opposite to each other.

So, $\angle 6$ and $\angle 7$ are vertically opposite angles.

$\angle 6=\angle 7$ ($\because$Vertically opposite angles are equal)

Hence$\angle 6$ and $\angle 7$are equal because they are vertically opposite angles.