# Interior Angles of a Polygon

## Notes

### Interior Angles of a Polygon:

• The interior angles of a polygon are the angles that are inside the shape.

• According to the angle sum property of a polygon, if the polygon has n sides, there will be (n – 2) triangles inside.
Sum of all the interior angles of a polygon = (n − 2) × 180.

 Numberof sides Name of thepolygon Polygon Numberoftriangles Sum of interior angles 3 Triangle 1 Sum of all the interior angles of a polygon = (n − 2) × 180∘= (3 – 2) × 180∘= 1 × 180∘ = 180∘. 4 Quadrilateral 2 Sum of all the interior angles of a polygon = (n − 2) × 180∘= (4 – 2) × 180∘= 2 × 180∘ = 360∘. 5 Pentagon 3 Sum of all the interior angles of a polygon = (n − 2) × 180∘= (5 – 2) × 180∘= 3 × 180∘ = 540∘. 6 Hexagon 4 Sum of all the interior angles of a polygon = (n − 2) × 180∘= (6 – 2) × 180∘= 4 × 180∘ = 720∘. 7 Heptagon 5 Sum of all the interior angles of a polygon = (n − 2) × 180∘= (7 – 2) × 180∘= 5 × 180∘ = 900∘. 8 Octagon 6 Sum of all the interior angles of a polygon = (n − 2) × 180∘= (8 – 2) × 180∘= 6 × 180∘ = 1080∘. : : : : : n A figure with n sides (n - 2) 180° × (n - 2)
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