Understanding and Calculating Interior Angles of Polygons | Sum, Measure, and Relationships

Interior Angles

Interior angles are the angles formed inside a polygon when two sides of the polygon are extended and intersect

Interior angles are the angles formed inside a polygon when two sides of the polygon are extended and intersect. In other words, the interior angles are the angles that you find inside the shape.

For a polygon with n sides (or vertices), the sum of the interior angles can be calculated using the formula: (n-2) * 180 degrees. This means that the sum of the interior angles in a triangle (which has 3 sides) is 180 degrees, the sum of the interior angles in a quadrilateral (which has 4 sides) is 360 degrees, and so on.

To find the measure of each interior angle in a regular polygon, you can divide the sum of the interior angles by the number of sides. For example, in a regular hexagon (which has 6 sides), the sum of the interior angles is 720 degrees (6-2) * 180 degrees = 720 degrees. Therefore, each interior angle in a regular hexagon measures 720 degrees / 6 = 120 degrees.

In addition to finding the sum and measure of interior angles, it’s also important to understand the properties and relationships between them. For example, in a triangle, the sum of any two interior angles is always greater than the measure of the third angle. In a quadrilateral, the sum of all four interior angles is always 360 degrees. These properties and relationships can be helpful in solving various math problems involving polygons.

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