Chapter 1.4, Problem 20WE

To determine

To sketch: given angle and to use a protector to check accuracy.

Explanation of Solution

Given information:

Given angle $45°$ .

Calculation:

On $\overline{AH}$ in a given plane, choose any point O between A and H. Consider $\overline{OA}$ and $\overline{OH}$ and all the rays than can be drawn from O on one side of $\overline{AH}$ . These rays can be paired 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 $m\angle BOC=\left|x-y\right|$ .

Thus the figure can be drawn as shown below:

By taking a protector and put it over the $\angle AOB$ .

Superimpose the protector’s $\overline{OA}$ line with the drawn angle’s $\overline{OA}$ line.

Measure the angle by using the protector postulate.