Chapter 2, Problem 5CT

To determine

Value of $\angle COD$

Answer to Problem 5CT

  $\angle COD={30}^0$

Explanation of Solution

Given:

  $\overrightarrow{OB}$ is bisector of $\angle AOC$ and

  $\overrightarrow{OC}$ is the bisector of $\angle BOD$

  $m\angle AOC={60}^0$

Since $\overrightarrow{OB}$ is bisector of $\angle AOC$

Then, $\angle AOB=\angle BOC$

And $\overrightarrow{OC}$ is the bisector of $\angle BOD$

Then,

  $\angle BOC=\angle COD$

Therefore,

  $\begin{array}{l}\angle AOB=\angle COD\\ \Rightarrow \frac{1}{2}\angle AOC=\angle COD\\ \Rightarrow \angle COD=\frac{{60}^0}{2}={30}^0\\ \Rightarrow \angle COD={30}^0\end{array}$