Polygons: Formula and Examples  

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 just divide the sum of the interior angles or (n-2) × 180 by the number of sides or n

Example: To find the measure of an interior angle of a regular octagon, which has 8 sides, apply the formula above as follows:
( (8-2) × 180) /8 = 135°

What is the total number degrees of all interior angles of a triangle? Answer 180°

What is the total number of degrees of all interior angles of the polygon on the left? Answer 360° since the polygon on the left is really just two triangles and each triangle has 180°.

What is the sum measure of the interior angles of the polygon (a pentagon) on the left? Answer Use Interior Angle Theorem: (5-2)× 180= 3× 180= 540°.

What is sum of the measures of the interior angles of the polygon (a hexagon) on the left? Answer Use Interior Angle Theorem: (6-2)× 180= 4 × 180 = 720°.

1+2 +3 =360°

1+2 +3+ 4 =360°

1+2 +3 + 4+5 =360°