Solving the interior and exterior angle of a polygon

Solving the interior and exterior angle 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.