Question

$OC$ and $OD$ are two rays from point $O$ on straight line $AOB$. $\angle AOC=2x,\angle COD=3x,\angle BOC=5x$.
Find each angle : $\angle AOC,\angle COD,\angle DOB$

Answer 1

$\angle BOC=5x=\angle COD+\angle DOB$

$\Rightarrow 5x=3x+\angle DOB$

$\Rightarrow \angle DOB=2x$

Now $\angle AOC+\angle COD+\angle DOB={180}^o$

$\because AOB$ is

$\Rightarrow 2x+3x+2x={180}^o$

$\Rightarrow 7x={180}^o$

$\Rightarrow x={\left(\frac{180}{7}\right)}^o$

$\Rightarrow \angle AOC=2x={\left(\frac{360}{7}\right)}^o$

$\angle COD=3x={\left(\frac{540}{7}\right)}^o$

$\angle DOB=2x={\left(\frac{360}{7}\right)}^o$