Question

In the given figure, $AOC$ is a straight line. If angle $AOB={50}^{\circ }$, angle $AOE={90}^{\circ }$ and angle $COD={25}^{\circ }$. Find the measures of:

(v). Reflex angle $COE$

Answer 1

Step 1: Finding the measure of $\angle BOC$

From figure, $\angle AOB={50}^{\circ }\angle AOE={90}^{\circ }$

To find : Reflex $\angle COE$



Now, $\because AOC$ is a straight line

$\Rightarrow \angle AOC={180}^{\circ }$

$\therefore \angle AOB+\angle BOC={180}^{\circ }$

$\Rightarrow {50}^{\circ }+\angle BOC={180}^{\circ }$ [Given]

$\Rightarrow \angle BOC={180}^{\circ }-{50}^{\circ }$

$\Rightarrow \angle BOC={130}^{\circ }$

Step 2: Finding the measure of Reflex $\angle COE$

Now,
Reflex $\angle COE$ = $\angle AOB+\angle BOC$
Reflex $\angle COE={130}^{\circ }+{150}^{\circ }+{190}^{\circ }$
$\therefore \angle COE={270}^{\circ }$

Hence reflex $\angle COE$ is ${270}^{\circ }$