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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