Question

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

(iii).Obtuse angle $BOD$

Answer 1

Step : Finding the measure of $\angle BOD$

Given: $\angle COD={25}^{\circ }$

To find: $\angle BOD$



Now, $\because AOC$ is a straight line

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

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

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

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

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

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

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

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

Hence, obtuse angle $\angle BOD$ is ${155}^{\circ }$.