Each interior angle ã in a regular ñ-gonna has a measure of ã = 20ñ. How many sides does the polygon have?

Question

Each interior angle ã in a regular ñ-gon has a measure of ã = 20ñ. How many sides does the polygon have?

Answer 1

n is the number of sides of the polygon.  In order for a closed shape to be a regular polygon the number of sides must be at least 3.

 

In a closed polygon, the number of sides always equals the number of interior angles.  Using the sum of interior angles formula

 

Sum of interior angles = 180(n - 2)

 

Sum of interior angles = 180((a/20) - 2)

 

Sum of interior angles = 9a - 360

 

 

You need the sum of interior angles, which you did not put in your question.  Once you have your sum of interior angles, you can solve for a.

 

Then you will divide the value of a by 20 to get n.