Question

In the adjoining figure, $AOB$ is a straight line. Find the value of $x$. Also, find $\angle AOC$ and $\angle BOD.$

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Answer 1

As $AOB$ is a straight line, the sum of angles on the same side of $AOB$, at a point $O$ on it is ${180}^{\circ }.$
Therefore,
$\angle AOC+\angle COD+\angle BOD={180}^{\circ }$

$\Rightarrow (3x-5{)}^{\circ }+{55}^{\circ }+(x+{20}^{\circ })={180}^{\circ }$

$\Rightarrow 4x={110}^{\circ }$

$\Rightarrow x={27.5}^{\circ }$
Hence,
$\angle AOC=3x-6$

$=3\times 27.5-6={76.5}^{\circ }$

and, $\angle BOD=x+20$

$=27.5+20={47.5}^{\circ }$