Question:
In the adjoining figure, AOB is a straight line. Find the value of x. Hence, find ∠AOC and ∠BOD.
Solution:
As $A O B$ is a straight line, the sum of angles on the same side of $A O B$, at a point $O$ on it, is $180^{\circ}$.
Therefore,
$\angle \mathrm{AOC}+\angle \mathrm{COD}+\angle \mathrm{BOD}=180^{\circ}$
$\Rightarrow(3 x-7)^{\circ}+55^{\circ}+(x+20)^{\circ}=180$
$\Rightarrow 4 x=112^{\circ}$
$\Rightarrow x=28^{\circ}$
Hence,
$\angle \mathrm{AOC}=3 x-7$
$=3 \times 28-7$
$=77^{\circ}$
and $\angle \mathrm{BOD}=x+20$
$=28+20$
$=48^{\circ}$