Maharashtra State BoardSSC (English Medium) 7th Standard
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Interior Angles of a Polygon

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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.

Number
of sides
Name of the
polygon
Polygon Number
of
triangles
Sum of interior angles
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.
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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