Solve the following:The sum of interior angles of a polygon is three times the sum of its exterior angles. Determine the number of sides of the polygon.

Given:  The sum of interior angles of a polygon is three times the sum of its exterior angles.

To find: We have to determine the number of sides of the polygon.

Solution: The sum of exterior angles of any polygon is $360$

Let the number of sides of the required polygon be n.

Sum of interior angles of the polygon of n sides = $2n - 4 * 90 = 3 \times 360$ 

$2n - 4 = 3 \times \frac{360}{90}$ = $12$ or $2n = 4 + 12 = 16$ or $n = \frac{16}{2}$ = 8

So the required polygon has 8 sides. It is an octagon.

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Updated on: 10-Oct-2022

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