Angles in Polygons

Angles in polygons are the angles formed by the intersection of two adjacent sides of the polygon. There are two main types of angles associated with polygons: interior angles and exterior angles.

Interior Angles

The angle of a polygon is referred to as the space formed at the intersection point (vertex) of two adjacent sides. Now, the interior angle of a polygon is the one that lies inside the polygon. The number of angles in a polygon having “n” sides is “n”. For example, a triangle has three sides, so it has three interior angles.

We know that a polygon is of two types of the polygon: a regular polygon and an irregular polygon. The measurement of all interior angles is the same, whereas in an irregular polygon the measurement of each angle may differ. In the figure given below, ABCD is a square whose interior angles are ∠1, ∠2, ∠3, and ∠4.

Read More about Interior Angles of a Polygon

Exterior Angles

The angle that lies at the outside of a polygon, which is formed by one side of the polygon and the extension of the other side, is referred to as the exterior angle of a polygon. The sum of an adjacent interior angle and exterior angle is equal to 180°. And the sum of all the exterior angles of a polygon is always equal to 360°.

Exterior angle of a regular polygon = 360° ÷ number of sides = 360°/n

Polygon is defined as a two-dimensional geometric figure that has a finite number of line segments connected to form a closed shape. The line segments of a polygon are called edges or sides, and the point of intersection of two edges is called a vertex. The angle of a polygon is referred to as the space formed at the intersection point (vertex) of two adjacent sides.

A polygon is of two types: a regular polygon and an irregular polygon. A regular polygon is a polygon whose all sides and all interior angles are measured the same, whereas an irregular polygon is a polygon whose all sides and all interior angles do not measure the same. And we also have different types of polygons like triangles, quadrilaterals, pentagons, hexagons, etc, based on the number of sides of a polygon. Every polygon has interior angles and exterior angles, where an interior angle is the one that lies inside the polygon and the exterior angle is the one that lies outside the polygon.