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4. What is a regular polygon? State the name of a regular polygon of

(a) 4 sides (b) 6 sides (c) 10 sides
5. Find the number of diagonals for
(a) a heptagon (b) a nonagon (c) a decagon
6. How many diagonals does a regular quadrilateral have?

7. Draw a hexagon PQRSTU and mark the following points.
(a) A, B and C in its exterior (b) X, Y and Z in its interior (c) G, H and I on its boundary

Angle Sum Property of Polygons

Interior angles of a polygon are the angles inside the shape. These are the angles
formed between two sides of a polygon.
We know that the sum of the measures of the interior angles of a triangle is 180°.
We can calculate the sum of the interior angles of a polygon by splitting it into
triangles and multiplying the number of triangles by 180°.

The number of triangles a polygon can be split into is always 2 less than the number of sides it has.

180° 180°

For example, Heptagon 180° 180° × 5 = 900°

180°
180°
A heptagon has 7 sides. So, we can split the heptagon into 5 triangles (7 – 2 = 5).
\ The sum of the interior angles of a heptagon = 5 × 180° = 900°

Thus, we can formulate the sum of interior angles as:
The sum of interior angles of a polygon = (n – 2) × 180°, where n = number of sides of the polygon
and (n – 2) is the number of triangles in the polygon.

Example 4: Find the sum of interior angles of the following polygons having:
(a) 5 sides (b) 8 sides

Solution: We have, the sum of interior angles of a polygon = (n – 2) × 180°, where n = number of
sides of the polygon.
(a) Sum of the interior angles of a 5-sided polygon (pentagon) = (5 – 2) × 180° (Q n = 5)

= 3 × 180° = 540°
(b) Sum of the interior angles of an 8-sided polygon (octagon) = (8 – 2) × 180° (Q n = 8)

= 6 × 180° = 1080°
To find each interior angle of a regular polygon, divide the sum of interior angles by the number
of sides in the polygon. Therefore,
Sum of interior angles of the polygon
Each interior angle of a regular polygon =
Number of sides
( n − ) × 180 °
2
If there is a regular polygon of ‘n’ sides, then each interior angle of the regular polygon =
n

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