Chapter 1, Problem 3CT

To determine

To verify: if the conclusion “ $\angle AXC$ is a straight angle” is true.

Answer to Problem 3CT

Yes

Explanation of Solution

Given:

The figure below:

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,

  $m\angle AXC=m\angle AXD+m\angle DXC$ ….. (1)

Now, the angles $\angle AXD$ and $\angle DXC$ sum up to form the straight line $\overleftrightarrow{AC}$ .

So,

  $\begin{array}{c}m\angle AXD+m\angle DXC=180°\\ m\angle AXC=180°\end{array}$

And thus $\angle AXC$ is a straight angle.