Question

In figure $\angle AOC\text{and}\angle BOC$ form a linear pair. if $a-2b={30}^{\circ }$ find $a\text{and}b$?

Answer 1

Given : $\angle AOC\text{and}\angle BOC$ form a linear pair and $a-2b={30}^{\circ }$

Since, $\angle AOC\text{and}\angle BOC$ form a linear pair
$\Rightarrow \angle AOC+\angle BOC={180}^{\circ }$

$\Rightarrow a+b={180}^{\circ }\left(1\right)$
Also $a-2b={30}^{\circ }\left(2\right)$

Subtracting equation $\left(2\right)$ from $1$, we get
$(a+b)-(a-2b)={180}^{\circ }-{30}^{\circ }$
$\Rightarrow 3b={150}^{\circ }$
$\Rightarrow b=\frac{{150}^{\circ }}{3}$
$\Rightarrow b={50}^{\circ }$
Since, $a-2b={30}^{\circ }$
$\Rightarrow a-2\left({50}^{\circ }\right)={30}^{\circ }$
$\Rightarrow a={30}^{\circ }+{100}^{\circ }$
$\Rightarrow a={130}^{\circ }$

Hence the values of $a\text{and}b$ are ${130}^{\circ }\text{and}{50}^{\circ }$ respectively.