Question

$\overrightarrow{OB}$is the bisector of $\angle AOC$and $\overrightarrow{OC}$is the bisector of $\angle BOD$. $m\angle AOC=60$. Find$m\angle COD$

Short answer

$m\angle COD={30}^{\circ }$

Step-by-step solution

Step 1. State the information.

$\overrightarrow{OB}$is the bisector of $\angle AOC$.

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

$m\angle AOC={60}^{\circ }$

Step 2. Show the calculation.

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

Then, $\angle AOB=\angle BOC$.

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

$\angle BOC=\angle COD$

Then, $\angle BOC=\angle COD$.

Therefore,

$\begin{array}{c}\angle AOB=\angle COD\\ \frac{1}{2}\angle AOC=\angle COD\\ \angle COD=\frac{{60}^{\circ }}{2}\\ ={30}^{\circ }\end{array}$

Step 3. State the conclusion.

Therefore, $\angle COD={30}^{\circ }$.