Understanding the Polygon Interior Angles Theorem | Finding the Sum of Interior Angles in Polygons

Polygon Interior Angles Theorem

The Polygon Interior Angles Theorem states that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees

The Polygon Interior Angles Theorem states that the sum of the interior angles of a polygon with n sides is equal to (n-2) times 180 degrees.

In simpler terms, if you have a polygon with n sides (where n is a whole number greater than 2), you can find the sum of all the interior angles by multiplying (n-2) by 180 degrees.

For example, let’s consider a triangle, which is a polygon with 3 sides. Using the formula, we can calculate the sum of the interior angles as (3-2) * 180 = 180 degrees. This means that the three interior angles in a triangle will always add up to 180 degrees.

Similarly, for a quadrilateral (4-sided polygon), the sum of the interior angles would be (4-2) * 180 = 360 degrees. Thus, the four interior angles in a quadrilateral will always add up to 360 degrees.

This theorem is not limited to specific polygons and can be applied to any polygon, regular or irregular, convex or concave, as long as it has more than 2 sides.

By knowing the sum of the interior angles and having the value of one angle, you can also find the value of the other interior angles in the polygon by dividing the sum by the number of angles.

Overall, the Polygon Interior Angles Theorem is a helpful concept in geometry as it allows us to determine the sum or individual measurements of interior angles in different polygons without having to calculate each angle individually.

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