Interior Angles
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Exterior Angles
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About Polygon Angles
Polygons are 2D shapes with straight sides. The angles inside (interior) and outside (exterior) of polygons follow specific rules:
The sum of interior angles in any n-sided polygon is given by the formula:
Sum = (n - 2) × 180°
For example, a pentagon (5 sides) has interior angles that sum to (5-2)×180° = 540°.
Sum = (n - 2) × 180°
For example, a pentagon (5 sides) has interior angles that sum to (5-2)×180° = 540°.
The sum of exterior angles for any polygon is always 360°, regardless of the number of sides.
For regular polygons, each exterior angle is 360° divided by the number of sides.
For regular polygons, each exterior angle is 360° divided by the number of sides.
Regular polygons have all sides and angles equal.
Irregular polygons have sides and/or angles of different measures.
While the angle sum formulas apply to both, individual angles can only be calculated directly for regular polygons.
Irregular polygons have sides and/or angles of different measures.
While the angle sum formulas apply to both, individual angles can only be calculated directly for regular polygons.
Did You Know?
The word "polygon" comes from the Greek words "poly" (many) and "gonia" (angle). The names of polygons are based on Greek numbers combined with "-gon" (e.g., pentagon, hexagon).