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.

1. Start with a triangle and click “Make Regular”
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.

Answer the following questions.

• To find the sum of angles of a polygon, the formula is _?__.
  
  Interactive popup. Assistance may be required.

  Check Your Answer

  S = ( n - 2 ) · 180

• To find the number of degrees of one angle of a regular polygon?
  
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  Check Your Answer

  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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  Check Your Answer

  s = (n - 2) · 180 n
  
  
  
• A quadrilateral has Interactive button. Assistance may be required. _____ 4 sides.
  The sum of the interior angles is Interactive button. Assistance may be required. _____ 360 degrees.
  If  the quadrilateral is regular, it has Interactive button. Assistance may be required. _____ 4 congruent angles that each measure Interactive button. Assistance may be required. _____ 90 degrees. In order to find the measure of each angle of a regular quadrilateral, Interactive button. Assistance may be required. _____ divide the sum of the angles by the number of angles; divide 360 by 4 . Another name for a regular quadrilateral is aInteractive button. Assistance may be required. _____ square .

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.