Chapter 1.4, Problem 19WE

To determine

To draw: The angle without measuring.

Explanation of Solution

Given information:

  

Formula used:

  $m\angle BOC=\left|x-y\right|$

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 $m\angle BOC=\left|x-y\right|$

  

Thus, the figure is shown below,

Here, $\angle AOB={90}^{\circ }$

By taking a protector and put it over the $\angle AOB$ . Superimpose the protector’s $\overline{OA}$ line with the drawn angles $\overline{OA}$ line. Measure the angle by using the protector postulate.

Conclusion:

Superimpose the protector’s $\overline{OA}$ line with the drawn angles $\overline{OA}$ line. Measure the angle by using the protector postulate.