In this section, you will find the measure of each interior angle of several regular polygons and then develop an algebraic representation for the measure of each interior angle of any regular polygon.

To explore the relationship of sides and the measure of each interior angle of regular polygons, click on the picture and follow the directions below. This will open a new webpage.

2. Complete the table below by recording the measure of each interior angle and filling in the process column.

Scroll over the chart to see the answers.

• To find the sum of angles of a polygon, the formula is _?__.
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S = ( n - 2 ) · 180
• To find the number of degrees of one angle of a regular polygon?
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Divide the sum of the interior angles by the number of angles in the polygon.
• What is the equation for finding an interior angle of a regular polygon?
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s = (n - 2) · 180 n

• A quadrilateral has _____ sides.
The sum of the interior angles is _____ degrees.
IfÂ  the quadrilateral is regular, it has _____ congruent angles that each measure _____ degrees. In order to find the measure of each angle of a regular quadrilateral, _____ . Another name for a regular quadrilateral is a _____ .

To verify your equation, enter it into “Y1=” in your graphing calculator and then go to the table to verify that the table in your calculator matches the table above.