Angles in Concave Polygon

Like any 2d geometric object, polygons can have interior as well as exterior angles.

• Interior Angle: An interior angle is an angle formed between two adjacent sides of a polygon, measured inside the polygon.
• Exterior Angle: An exterior angle of a polygon is an angle formed between one side of the polygon and the extension of an adjacent side, measured outside the polygon.

Sum of Exterior Angles of a Concave Polygon

In a polygon with n sides, each exterior angle corresponds to one interior angle. The sum of the exterior angles of any polygon, regardless of the number of sides, is always 360°.

Thus, for concave polygon sum of all exterior angle is 360°.

Sum of Interior Angles of a Concave Polygon

The sum of the interior angles of a concave polygon can be found by using the same formula as: (n-2) × 180°, Here “n” is the number of sides.

Example: Find the sum of the interior angles of a concave polygon with 7 sides.

Solution:

Given: n = 7

Sum of the Interior Angles = (n-2) × 180°

⇒ Sum of the Interior Angles = (7-2) × 180°

⇒ Sum of the Interior Angles = 5 × 180° = 900°

Concave Polygon is a type of polygon with at least one interior angle that is larger than 180°. In other words, a concave polygon has at least one “dent” or indentation in its boundary. In this article, we will learn about Concave Polygon in detail including their properties as well as formulas related to it’s interior as well as exterior angles.