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:

(iv). Reflex angle $BOD$

Answer 1

Step : Finding the measure of reflex $\angle BOD$

$\because AOC$ is a straight line.

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



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

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

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

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

$\therefore \angle BOC={130}^{\circ }$ and $\angle COD={25}^{\circ }$

$\Rightarrow \angle BOD=\angle BOC+\angle COD$

$\Rightarrow \angle BOD={130}^{\circ }+{25}^{\circ }={155}^{\circ }$

Now, reflex angle $BOD={360}^{\circ }-\angle BOD$

$\Rightarrow$ reflex angle $BOD={360}^{\circ }-{155}^{\circ }={205}^{\circ }$

Hence, reflex angle $BOD$ is ${205}^{\circ }$.