Question

In the given figure, $AOC$ is a straight line.If $angleAOB={50}^{\circ },angleAOE={90}^{\circ }andangleCOD={25}^{\circ }$. Find the measures of:

(i) angle $BOC$

Answer 1

Finding the measure of $\angle BOC$

Given : $\angle AOC$ is a straight line and $\angle AOB={50}^{\circ }$

To find : $\angle BOC$



Now,
$\because AOC\text{is a straight line}$
$\Rightarrow \angle AOC={180}^{\circ }$
$\therefore \angle AOB+\angle BOC={180}^{\circ }$
$\Rightarrow {50}^{\circ }+\angle BOC={180}^{\circ }$ , [Given]
$\Rightarrow \angle BOC={180}^{\circ }-{50}^{\circ }$
$\Rightarrow \angle BOC={130}^{\circ }\dots \left(i\right)$

Hence, $\angle BOC$ is ${130}^{\circ }$.