Question

$\angle A$ and $\angle B$ form a linear pair. If $m\angle A=x^o$ and $m\angle B=2x^o$, then the value of $x$ is .

Answer 1

$\underset{–}{\text{Given:}}$
$\bullet$$\angle A$ and $\angle B$ form a linear pair.
$\bullet$ $m\angle A=x^o$
$\bullet$ $m\angle B=2x^o$

$\underset{–}{\text{Linear Pair:}}$
Pair of adjacent angles whose non-common sides form a straight line and their measures add up to ${180}^o$.

$\because$ $\angle A$ and $\angle B$ form a linear pair.
$\Rightarrow$ $m\angle A+m\angle B={180}^o$
$\Rightarrow$ $x^o+2x^o={180}^o$
$\Rightarrow$ $3x^o={180}^o$
Dividing $3$ from both sides,
$\Rightarrow \frac{3x^o}{3}=\frac{{180}^o}{3}$
$\Rightarrow$ $x=60$

So, the value of $x$ is $60$.