Question

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

Answer 1

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

$\Rightarrow (3x-7{)}^{\circ }+{55}^{\circ }+(x+20{)}^{\circ }={180}^{\circ }$

$\Rightarrow (3x-7+55+x+20{)}^{\circ }={180}^{\circ }$

$\Rightarrow 4x+68=180$

$\Rightarrow 4x=180-68$

$\Rightarrow 4x=112$

$\Rightarrow x=\frac{112}{4}$

$\Rightarrow x=28$ ---(1)

Now, $\angle AOC=(3x-7{)}^{\circ }=(3\left(28\right)-7{)}^{\circ }=(84-7{)}^{\circ }={77}^{\circ }$

$\angle BOD=(x+20{)}^{\circ }=(28+20{)}^{\circ }={48}^{\circ }$