Chapter 11.3, Problem 40HP

a.

To determine

To describe the difference between a regular polygon and an irregular polygon.

Explanation of Solution

Given:

A regular polygon and an irregular polygon

A regular polygon is the one which has all sides and all the angles equal.

An irregular polygon is the one which does not have equal sides and equal angles.

Example:

  

b.

To determine

To explain the process used to find the interior angle measure of a regular polygon.

Explanation of Solution

Given:

A regular polygon

Formula used:

Sum of the interior angles of a polygon: ${180}^0\times \left(n-2\right)$ where $n$ is the number of sides of the given polygon.

Calculation:

Sum of the interior angles of a regular polygon is given by,

  $\Rightarrow {180}^0\times \left(n-2\right)$ …..(i).

Now for the measure of a single interior ange divide equation (i) by $n$ ,

  $\Rightarrow \frac{{180}^0\times \left(n-2\right)}{n}$

Conclusion:

Therefore, the measure of one interior angle $=\frac{\left(n-2\right)\times 180}{n}.$