Question

In the adjacent figure. $\overleftrightarrow{AB}$ is a straight line. Find the value of x and also find $\angle AOC,\angle COD$ and $\angle BOD$.

Answer 1

Since $\overleftrightarrow{AB}$ is a straight line.

So, the sum of all the angles on $\overleftrightarrow{AB}$ at a point O is 180${}^o$.
$\Rightarrow (3x+7{)}^{\circ }+(2x-19{)}^{\circ }+x={180}^{\circ }$ (Linear angles)
$\Rightarrow 6x-12=180$

$\Rightarrow 6x=192$

$\Rightarrow x=\frac{192}{6}$

$\Rightarrow x=32$
So, $\angle AOC=(3x+7{)}^{\circ }=(3\times 32+7{)}^{\circ }={103}^{\circ }$,
$\angle COD=(2x-19{)}^{\circ }=(2\times 32-19{)}^{\circ }={45}^{\circ }$

and $\angle BOD={32}^{\circ }$