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The sum of all exterior angles of a polygon is __________. Fill in the blanks to make the statement true.

Solution:

Given, The sum of all exterior angles of a polygon is __________.

We have to fill in the blanks to make the statement true.

Consider a pentagon

The sum of all exterior angles of a polygon is __________

Let a, b, c, d, e be the exterior angles of the polygon

Let 1, 2, 3, 4 and 5 are the interior angles of the polygon.

We know that the sum of all the interior angles of the polygon is (n - 2) x 180°

where n is the number of sides present in the polygon.

Here, n = 5

Sum of interior angles = (5 - 2) × 180°

= 3 × 180°

So, ∠1 + ∠2 + ∠3 + ∠4 + ∠5 = 540°

We know that the sum of the linear angle is 180 degrees.

So, ∠a + ∠5 = 180°

∠a = 180° - ∠5

Similarly, ∠b = 180° - ∠1

∠c = 180° - ∠2

∠d = 180° - ∠3

∠e = 180° - ∠4

Sum of exterior angles = a + b + c + d + e

= 180° - ∠5 + 180°- ∠1 + 180° - ∠2 + 180° - ∠3 + 180° - ∠4

= 5(180°) - (∠1 + ∠2 + ∠3 + ∠4 + ∠5)

= 900° - 540°

= 360°

Therefore, the sum of exterior angles of the polygon is 360 degrees.

✦ Try This: The sum of all interior angles of a polygon is given by __________. Fill in the blanks to make the statement true.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 5 Problem 70

Summary:

The sum of all exterior angles of a polygon is 360 degrees.

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