Question

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

(ii) angle $EOD$

Answer 1

Finding the measure od $\angle EOD$

Given: $AOC$ is a straight line.

$\angle COD={25}^{\circ }and\angle AOE={90}^{\circ }$

To find: $\angle EOD$

Now,
$\because AOC$ is a straight line


$\Rightarrow \angle AOC={180}^{\circ }$
$\Rightarrow \angle AOE+\angle EOD+\angle COD={180}^{\circ }$
$\left[fromfigure\right]$

$\Rightarrow {90}^{\circ }+\angle EOD+{25}^{\circ }={180}^{\circ }$
$\Rightarrow \angle EOD={180}^{\circ }-{90}^{\circ }-{25}^{\circ }$
$\therefore \angle EOD={65}^{\circ }$

Hence $\angle EOD$ is ${65}^{\circ }$