Interior Angle Formula

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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Interior Angle Formula

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