Are The Outside Angles Of Polygons Always The Same?

The sum of an interior angle and its corresponding exterior angle is always 180 degrees, as they lie on the same straight line. In a polygon, the exterior angles are the angles between any side of the shape and a line extended from the next side. For regular polygons, all the exterior angles are the same, adding to 360°.

There are two important theorems involving exterior angles: the Exterior Angle Sum Theorem and the Exterior Angle Theorem. The Exterior Angle Sum Theorem states that the exterior and interior angles are measured from the same line, so they add up to 180°. The sum of exterior angles of a polygon is equal to 360°, and any flat shape or figure is said to have interior or exterior angles only if it is a closed polygon.

Exterior angles of a polygon are formed when by one of its sides and extending the other side. The sum of all the exterior angles in a polygon is equal to 360°. The number of angles/vertices is also important. If the polygon is regular, all of its exterior angles will be the same measure, and all the little changes in direction must add up to 360 degrees.

In the case of convex polygons, where all vertices point “outwards” away from the interior, the exterior angles are always on the outside of the polygon. If an object has a different Gaussian curvature, that has an effect on the sum of all inner angles and because of that, also on outer angles.