Question

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

Answer 1

AOB is a straight line. Therefore,
$$\begin{gathered} \angle AOC+\angle COD+\angle BOD=180° \\ \Rightarrow \left(3x+7\right)°+\left(2x-19\right)°+x°=180° \\ \Rightarrow 6x=192° \\ \Rightarrow x=32° \end{gathered}$$
Therefore,
$$\begin{gathered} \angle AOC=3\times 32°+7=103° \\ \angle COD=2\times 32°-19=45°\mathbf{}\mathrm{and} \\ \angle BOD=32° \end{gathered}$$