Question

Fill in the blanks :

If $\angle 7=45°$, then $\angle 6=$…………

Answer 1

Linear Pair :

A linear pair can be defined as two adjacent angles that add up to $180°$ or two angles that form a line or a straight angle when combined together. As shown in the given figure :

So, $\angle 1$ and $\angle 2$ form a linear pair.

Similarly, as per the question :

$\angle 7$ and $\angle 6$ form a linear pair.

$\angle 7+\angle 6=180°$ ($\because$Linear pair adds up to $180°$)

$\Rightarrow 45°+\angle 6=180°$ (As given $\angle 7=45°$)

$\Rightarrow \angle 6=180°-45°$ (By transposing $45°$ from L.H.S. to R.H.S.)

$\Rightarrow \angle 6=135°$

Hence the measure of $\angle 6$ is $135°$, i.e. $\angle 6=135°$.