The interior angles of a regular polygon are all equal. What is the measure of each interior angle of an n-sided polygon?
Thank you!
180/3 = 60 degreees for three sides (triangle)
360/4 = 90 for four sides (a square)
540/5 = 108 for five sides (a regular pentagon)
720/6 = 120 for a six sides
etc...
(n-2)*180/n = 180 - 360/n for n sides
To find the measure of each interior angle of a regular polygon with n sides, you can use the formula:
Measure of each interior angle = (n-2) * 180 / n
In this formula, "n" represents the number of sides of the polygon.
For example, if you have a pentagon (a polygon with 5 sides), you can substitute the value of n into the formula:
Measure of each interior angle = (5-2) * 180 / 5
Simplifying this equation:
Measure of each interior angle = 3 * 180 / 5 = 540 / 5 = 108 degrees
So, each interior angle of a regular pentagon measures 108 degrees.
Similarly, for other regular polygons, you can substitute the value of n into the formula to find the measure of each interior angle.