Learn The Formulas For Interior Angles Of A Polygon

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.

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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.

Solved Examples Using Interior Angle Formula

1. 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°.

2. 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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