Question

In the figure, $\angle AOC$ and form a linear pair. If $a-2b={30}^{\circ }$, find $a$ and $b$.

Answer 1

Given: $\angle AOC$ and $\angle BOC$ form a linear pair

Therefore,

$\angle AOC+\angle BOC={180}^{\circ }$

$\Rightarrow a+b={180}^{\circ }$ [As $\angle AOC=a$ and $\angle BOC=b$]

$\Rightarrow a={180}^{\circ }-b$...(i)

Putting the value from (i) in $a-2b={30}^{\circ }$, we get,

$\Rightarrow {180}^{\circ }-b-2b={30}^{\circ }$

$\Rightarrow -3b=-{150}^{\circ }$

$\Rightarrow b=\frac{{150}^{\circ }}{3^{\circ }}={50}^{\circ }$

Therefore,

$a={180}^{\circ }-{50}^{\circ }={130}^{\circ }$

Hence,$\angle AOC={130}^{\circ }$ and $\angle BOC={50}^{\circ }$