Polygon Interior Angle Sum Theorem

An octagon has 8 sides.

Polygon interior angle sum theorem. In a polygon of n sides the sum of the interior angles is equal to 2n 4 90. Find the sum of the interior angles of a heptagon 7 sided solution. In order to find the measure of a single interior angle of a regular polygon a polygon with sides of equal length and angles of equal measure with n sides we calculate the sum interior anglesor red n 2 cdot 180 and then divide that sum by the number of sides or red n.

An exterior angle of a polygon is formed by extending only one of its sides. If a convex polygon has n sides then its interior angle sum is given by the following equation. The polygon angle sum theorems algebra find the missing angle measures.

If at least one angle of a polygon is greater than 1800. The formula for interior angles can also be used to determine how many sides a polygon has if you know the sum of the angles. Make sure each triangle here adds up to 180 and check that the pentagon s interior angles add up.

The polygon in figure 1 has seven sides so using theorem 39 gives. Consider the sum of the measures of the exterior angles for an n gon. Polygons interior angles theorem.

This is the interior angle sum theorem. Suppose you have a polygon whose interior angles sum to 540 degrees. Find the sum of the measures of the interior angles of an octagon.

Its interior angles add up to 3 180 540 and when it is regular all angles the same then each angle is 540 5 108 exercise. Round to the nearest tenth if necessary. A pentagon has 5 sides and can be made from three triangles so you know what.