Q19 - Geometry

Question

State the measure of each angle.

• $\angle FOG$
  

Step-by-Step Solution

Answer

The measure $\angle FOG$ of is $40°$.

Step 1. Apply protractor postulate.

On $\overline{AH}$ in a given plane, choose any point O between A and B.

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

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 $\overline{OF}$ is paired with x, and $\overline{OG}$ with y, then $m\angle FOG=\left|x-y\right|$.

Step 2. Observe the figure below and write the values of OF and OG.

It can be observed from the figure that, $\overline{OF}$ is 120 and $\overline{OG}$ is 160.

Step 3. Calculate m∠FOG

$\begin{array}{l}m\angle FOG=\left|120-160\right|\\ =\left|-40\right|\\ =40°\end{array}$