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

The sum of interior angles of a polygon = (n – 2) × 180° …..(i)

The Sum of exterior angle of a plygon is 360°

According to the question:

Sum of interior angles = 3 × sum of exterior angles

Sum of interior angles = 3 × 360° = 1080°

Now applying relation as per equation (i)

(n – 2) × 180° = 1080°

n – 2 = n – 2 = 6

n = 6 + 2 = 8

Therfore numbers of sides in the polygon are 8.

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