Chapter 1.4, Problem 19CE

To determine

The measure of the angle $\angle FOG$

Answer to Problem 19CE

40°

Explanation of Solution

Given information:

  

Formula used:

The measure of angles from 0 to 180

Calculation:

Consider the protector postulate:

  $\overline{AH}$ in a given plane is considered.

Any point O between A and H is chosen.

Consider $\overline{OA}\text{and}\overline{OH}$ and all these rays are drawn from O on one side of $\overline{AH}$ .

These rays results in pairing with the real numbers 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 $\overline{OC}$ with y, then $m\angle BOC=\left|x-y\right|$

  

From the above figure it can be observe that $\overline{OF}$ is 120 and $\overline{OG}$ is 160.

Thus,

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

Therefore, the required angle is 40°.

Conclusion:

The required angle is 40°.