Chapter 1.5, Problem 7ST2

To determine

To complete: $m\angle HOK=\_\_\_$ and $\angle HOK$ is called a(n) ______ angle.

Answer to Problem 7ST2

  $m\angle HOK=180°$ and $\angle HOK$ is called a straight angle.

Explanation of Solution

Given:

The figure:

Concept Used:

Angle addition postulate:

If point B lies in the interior of $\angle AOC$ , then

  $m\angle AOB+m\angle BOC=m\angle AOC$

The sum of all angles on a straight line is $180°$ and such an angle is called straight angle.

From the Angle addition postulate, it can be said that,

  $m\angle HOK=m\angle HOJ+m\angle JOK$ ….. (1)

Now, the angles $\angle HOJ$ and $\angle JOK$ sum up to form the straight line $HOK$ .

So,

  $\begin{array}{c}m\angle HOJ+m\angle JOK=180°\\ m\angle HOK=180°\end{array}$

And thus $\angle HOK$ is called a straight angle.