Question

Which of the following can never be the measure of exterior angle of a regular polygon?

• A. $22°$
• B. $36°$
• C. $45°$
• D. $30°$

Answer 1

The correct option is A

$22°$

Step 1. Explanation for the correct option.

Sum of exterior angles of a polygon $=360°$

And number of sides, $n=\frac{360°}{\mathrm{exterior}\mathrm{angle}}$

Thus, $\frac{360°}{22°}=16.3636$ which is not a whole number.

So $22°$ can not be the measure of exterior angle of a regular polygon.

Step 2. Explanation for the incorrect options.

Since,

$$\begin{gathered} \frac{360°}{36°}=10 \\ \frac{360°}{45°}=8 \\ \frac{360°}{30°}=12 \end{gathered}$$

Which is a whole number. So these angle can be the measure of exterior angle of a regular polygon.

Hence, the correct option is $\mathrm{A}$.