# 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.

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

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