interior angle of a regular n-gon

in general, the measure of an interior angle of a regular n-gon is




The sum of the measures of the interior angles of a triangle is 180 degrees.

Since all the sides of equilateral triangles are the same length, all the angles are the same...




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Measuring Interior Angles of a Polygon

Step 1

Determine whether the polygon you are working with is regular or irregular.A regular polygon is a polygon whose sides and angles are all of the same measure, all other polygons are irregular.

Step 2

Use the equation 180*(n-2), if you are dealing with a regular polygon, where n is the number of sides that the polygon has, to determine the sum of the interior angles of the polygon. Then to determine the measurement of the interior angles of that regular polygon you would simply divide the sum of the interior angles by n, since that is the number of sides and angles of the regular polygon. The resulting number will be the measurement of all the interior angles of that polygon.

Step 3

Use the measurements provided for you, if you are working with an irregular polygon. If the interior angle measurements aren't provided for you then you can use a protractor to determine the measurements of the interior angles.
Calculating the Sum of the Exterior Angles of a Polygon

Step 1

Subtract the measurement of each interior angle from 180 to get the measurement of the corresponding exterior angle.If you were to draw a continuous straight line off of each side of the polygon then you would be able to see not only the interior angles but also the exterior angles. We know that a straight line as a measurement of 180 degrees, so, if you subtract the measurement of the interior angle from 180 (the total degrees of the straight line) then what you are left with is the measurement of the exterior angle. In math terms, exterior and interior angles are supplementary to each other.This is the procedure that you follow for both regular and irregular polygons.

Step 2

Add the measurements of all the exterior angles together to get the sum of the exterior angles of the polygon.You should get 360 degrees because that is the sum of the exterior angles of all polygons.

Step 3

Use the knowledge that the sum of the exterior angles of any polygon is always going to 360 degrees to make finding the measurements of the exterior angles of a polygon easier next time around.

Step 4

Determine the measurement of its exterior angles by dividing 360 by the number of sides of the polygon when you are dealing with a regular polygon.

Step 5

Determine the measurement of a particular exterior angle, if you have the measurements of all the other exterior angles, by adding up the measurements off all the other exterior angles and then subtracting that number from 360 when dealing with an irregular polygon.