# Problems on Angle Sum Property of a Polygon

We will learn how to solve the problems on angle sum property of a polygon having 'n' sides. We know, the sum of 3 angles of a triangle is 180°.

1. Find the sum of all the interior angle of a polygon having 29 sides.

Solution:

We know that sum of all the interior angle in a polygon = (n - 2) × 180°

Here, n = 29

Therefore, the sum of all interior angles = (29 – 2) × 180°

= 27 × 180°

= 4860°.

2. If the sum of the measure of the interior angle of polygon is 3240, find the number of sides of the polygon.

Solution:

Let the number of sides of the polygon be n.

The sum of the interior angles = (2n – 4) right angles

But given sum of the interior angles = 3240

Therefore, (2n – 4) × 90° = 3240

⇒       2n – 4 = 3240/90

⇒       2n – 4 = 36

⇒            2n = 36 + 4

⇒            2n = 40

⇒              n = 40/2

⇒              n = 20

Therefore, the number sides of the polygon is 20.

3. Find the sum of interior angles of a decagon.

Solution:

We know, a decagon have 10 sides.

Therefore, n = 10

Sum of interior angles = (2n - 4) × 90°

= (2 × 10 - 4) × 90°

= (20 - 4) × 90°

= 16 × 90°

= 1440°

Therefore, the sum of interior angles of a decagon is 1440°.

4. Sum of all interior angles of a polygon is 3060°. How many sides does the polygon have?

Solution:

We know that sum of all the interior angles of a polygon = (n - 2) × 180°

According to the problem, we have

(n - 2) ×180 = 3060

⇒        (n - 2) = 3060/180

⇒          n – 2 = 17

⇒               n = 17 + 2

⇒               n = 19

Therefore, the polygon have 19 sides.

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Polygons

Polygon and its Classification

Terms Related to Polygons

Interior and Exterior of the Polygon

Convex and Concave Polygons

Regular and Irregular Polygon

Number of Triangles Contained in a Polygon

Angle Sum Property of a Polygon

Sum of the Exterior Angles of a Polygon