Chapter 1.4, Problem 21WE

To determine

The angle without measuring.

Explanation of Solution

Given information:

Using the protractor in checking the angle is ${150}^{\circ }\text{angle}$

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 raysresults in pairing with the real numbers from 0 to 180 in such a way that:

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 as

  

Here, $\angle AOB={150}^{\circ }$

Verification:

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.

The measure will be ${150}^{\circ }$

Conclusion:

The required angle is ${150}^{\circ }$