Question

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Answer 1

Question

In a polygon, sum of inner angles and sum of outer angles are equal. Find the number of sides of the polygon.

Given

• The sum of the inner angles and sum of outer angles of a polygon are equal.

To find

• Number of sides of the polygon

Concept

We are given that the sum of the inner angles and the sum of the outer angles of polygon is equal. As we know, the sum of the outer angles of polygon is 360°. So, we will keep it equal to the sum of the interior angles of the polygon.

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

Solution

Using formula,

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

where,

• n = number of sides.

Sum of the outer angles of polygon = 360°

According to the question,

Sum of inner angles = Sum of outer angles

⟶ (2n - 4) × 90° = 360°

⟶ 2n - 4 = 360°/90°

⟶ 2n - 4 = 4

⟶ 2n = 4 + 4

⟶ 2n = 8

⟶ n = 8/2

⟶ n = 4

Therefore, number of sides of the polygon is 4

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Let's verify :-

The sum of inner angles = Sum of outer angles

Using formula,

Sum of inner angles = (2n - 4) × 90°

⟶ (2 × 4 - 4) × 90°

⟶ (8 - 4) × 90°

⟶ 4 × 90°

⟶ 360°

Sum of the inner angles = 360°

It's equal to the sum of the outer angles of the polygon.

Hence, verified.