Interior Angle Formulae
The interior angle of a polygon is the one that lies inside the polygon. The interior angle of a polygon can be found in the following ways:
Using the Number of Sides
The measure of each interior angle of a regular polygon having n sides is given as follows:
I = [(n – 2) × 180° / n]
Where,
- I is the value of the interior angle, and
- n is the number of sides or number of angles of polygons.
Using Exterior Angle
We know that the sum of an adjacent interior angle and exterior angle is equal to 180°. So, when the exterior angle of a polygon is given, the polygon formula to determine the interior angle of a polygon is given as follows:
I = 180° – E
Where,
- I is the value of the interior angle, and
- E is the corresponding exterior angle for that interior angle.
Using Sum of Interior Angles
We know that all the interior angles of a regular polygon are equal. So, the measure of each interior angle of a regular polygon is equal to the sum of the interior angles of the polygon divided by the number of sides.
I = S / n
Where,
- S is the sum of interior angles, and
- n is the number of sides or number of angles of polygons
Sum of Angles in a Polygon
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.
Table of Content
- What is Polygons
- Angles in Polygons
- Interior Angles
- Exterior Angles
- Sum of Interior Angles of a Polygon
- Interior Angle Formulae
- Using the Number of Sides
- Using Exterior Angle
- Using Sum of Interior Angles
- Interior Angles of Regular Polygons
- Sum of Interior Angle of Polygon Theorem
- Solved Examples on Interior Angles Formula
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