Question

what are the properties of interior angles
​

Answer 1

Answer:

The sum of the internal angle and the external angle on the same vertex is 180°.

The sum of all the internal angles of a simple polygon is 180(n–2)°, where n is the number of sides.

More items...

Answer 2

• The sum of the internal angle and the external angle on the same vertex is 180°.
• The sum of all the internal angles of a simple polygon is 180(n–2)°, where n is the number of sides. The formula can be proved by using mathematical induction: starting with a triangle, for which the angle sum is 180°, then replacing one side with two sides connected at another vertex, and so on.
• The sum of the external angles of any simple convex or non-convex polygon, if only one of the two external angles is assumed at each vertex, is 360°.
• The measure of the exterior angle at a vertex is unaffected by which side is extended: the two exterior angles that can be formed at a vertex by extending alternately one side or the other are vertical angles and thus are equal.