Interior Angle Formula
Interior angle formulas are used to find interior angles associated with a polygon and their sum. Interior angles are the angles that lie inside a shape, generally a polygon. Also, the angles lying in the area enclosed between two parallel lines that are intersected by a transversal are also called interior angles. Let us understand the interior angle formula in detail in the following section.
What is Interior Angle Formula?
The interior angle formula is used to:
- find the sum of all interior angles of a polygon.
- find an unknown interior angle of a polygon.
- find each interior angle of a regular polygon.
Let us consider a polygon of n sides. Then by interior angle formula to find the sum of interior angles of a polygon is given as,
The sum of interior angles = 180(n-2)º
The interior angles of a polygon always lie inside the polygon and the formula to calculate it can be obtained in three ways.
Formula 1: For “n” is the number of sides of a polygon, formula is as,
Interior angles of a Regular Polygon = [180°(n) – 360°] / n
Formula 2: The formula to find the interior angle, if the exterior angle of a polygon is given,
Interior Angle of a polygon = 180° – Exterior angle of a polygon
Formula 3: If the sum of all the interior angles of a regular polygon, the measure of interior angle can be calculates using the formula,
Interior Angle = Sum of the interior angles of a polygon / n
where,
“n” is the number of polygon sides
Let us understand interior angle formulas better using solved examples.
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Example 1: Find the sum of all interior angles of a heptagon.
Solution: To find: The sum of all interior angles of a heptagon.
We know that the number of sides of a heptagon is, n = 7.
By interior angle formula
The sum of interior angles = 180(n-2)º
= 180 (7-2)º
= 180 (5)º= 900º
Answer: The sum of all interior angles of a heptagon = 900°.
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Example 2: Find the measure of each interior angle of a regular polygon of 23 sides. Round your answer to the nearest hundredths.
Solution:
To find: The measure of each interior angle of a regular polygon of 23 sides.
The number of sides of the given polygon is n = 23.
By interior angle formula,
The sum of interior angles = 180(n-2)º= 180 (23-2)º
= 180 (21) º
= 3780º
The measure of each interior angle is obtained by dividing the above sum by 23.
Each interior angle = 3780 / 23 = 164.35°
Answer: Each interior angle of a polygon of 23 sides = 164.35°.
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