Q17 - Geometry

Question

State the measure of each angle.

• $\angle BOC$
  

Step-by-Step Solution

Answer

The measure of $\angle BOC$ is $\mathbf{70}\mathbf{°}$.

Step 1. Apply protractor postulate

Consider rays, $\overline{OA}$ and $\overline{OH}$ which are drawn from point O on $\overline{OH}$. 

These rays’ results in pairing with the angles from 0 to 180 in such a way that:

The line $\overline{OA}$ is paired with 0, and $\overline{OH}$ with 180.

If $\overline{OB}$ is paired with x, and $\overline{OA}$ with y, then $m\angle BOC=\left|x-y\right|$.

Step 2. Observe the figure below and write the values of O B and O C .

It can be observed from the figure that, $\overline{OB}$ is $\overline{OC}$ and  is 90.

Step 3. Calculate m∠BOC

$\begin{array}{l}m\angle BOC=\left|20-90\right|\\ =\left|-70\right|\\ =70°\end{array}$