Angles in a Polygon

Polygons

• A polygon is a 2D shape with straight sides that are closed to form a loop.

• Examples: triangles, squares, pentagons, hexagons, etc.

Types of Angles in Polygons

• Interior Angles:

  • The angles inside the polygon formed by two adjacent sides.

• Exterior Angles:

  • The angles formed by extending one side of the polygon and measuring the angle outside the polygon.

Key Concepts

• Sum of Interior Angles:

  • The sum of the interior angles of an n-sided polygon can be calculated using the formula:

    • (n - 2) x 180°

    • where 'n' is the number of sides of the polygon.

• Sum of Exterior Angles:

  • The sum of the exterior angles of any convex polygon is always 360°.

• Regular Polygons:

  • A regular polygon has all sides and all angles equal.

  • To find the measure of each interior angle of a regular polygon:

    • Calculate the sum of interior angles using the formula above.

    • Divide the sum by the number of sides (n).