Question

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

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 $180°$.
Therefore,
$$\begin{gathered} \angle \mathrm{AOC}+\angle \mathrm{COD}+\angle \mathrm{BOD}=180° \\ \Rightarrow \left(3x-7\right)°+55°+\left(x+20\right)°=180 \\ \Rightarrow 4x=112° \\ \Rightarrow x=28° \end{gathered}$$
Hence,
$\angle \mathrm{AOC}=3x-7$
$$\begin{gathered} =3\times 28-7 \\ =77° \end{gathered}$$
and $\angle \mathrm{BOD}=x+20$
$$\begin{gathered} =28+20 \\ =48° \end{gathered}$$