What Is An Octagon’S Total Internal Angle?

The general rule states that the sum of interior angles in a regular polygon is equal to (n – 2) × 180°/n. In a regular octagon, the sum of internal angles is always 1080°, meaning each interior angle measures 1080°/8=135°. Each exterior angle for a regular octagon has an equal measure.

A regular octagon has 8 sides, so n = 8. Substituting 8 for n in the formula, the sum of the measures of the interior angles is 1080°. In irregular polygons, the sum of the interior angles would always be (n – 2) × 180°. Therefore, the sum of the interior angles of an octagon is (n – 2) × 180° = 1080°.

In a regular octagon, the interior angle at each vertex is 135°, and the central angle is 45°. The sum of the measures of the interior angles of an octagon is equal to (n – 2) × 180°.

To check this, one can check that all the exterior angles will total to 360°. Each interior angle of a regular octagon is equal to 135°, so the measure of the exterior angle becomes 180° – 135° = 45°. The sum of the interior angles of a regular octagon is equal to 1080°.