About Interior Angle Formula
Interior angle formulas are used to calculate the sum of interior angles associated with a polygon. The angles inside a shape, usually a polygon, are called interior angles. Interior angles are angles that lie within the space enclosed between two parallel lines that are intersected by a transversal. In the following section, we'll look at the interior angle formula in greater depth.
What do you mean by Interior Angle Formula?
- The formula for internal angles is used to:
- Determine the sum of all a polygon's internal angles.
- Determine a polygon's unknown inner angle.
- Determine each regular polygon's internal angles.
- Consider the case of a polygon with n sides. The total of interior angles of a polygon is then calculated using the interior angle formula, which is as follows:
- The sum of interior angles = 180(n - 2)°
- The interior angles of a polygon are always inside the polygon, and there are three techniques to calculate them.
- Formula: Interior angles of a Regular Polygon = [180°(n) – 360°] / n, where "n" is the number of sides of a polygon.
- Formula: If the exterior angle of a polygon is known, the formula for finding the interior angle is:
- a polygon's interior angle = 180° – a polygon's exterior angle
- Formula: The measure of interior angle can be calculated using the formula if the sum of all the interior angles of a regular polygon:
- Interior Angle = Sum of a polygon's interior angles / n
- Here, "n" is the number of polygon sides
Solved examples based on Interior Angle Formula
- Example: Find the sum of all interior angles of a heptagon.
- Sol:
- 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)°
- = 180 (7-2)°
- = 180 (5)° = 900°
- Answer: The sum of all interior angles of a heptagon = 900°.
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