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Question
The sum of the interior angles of a polygon is 6.5 times the sum of its exterior angles. Find the number of sides of the polygon.
Solution
Sum of the interior angles of a polygon = (n - 2) x 180°
Sum of the exterior angles of a polygon = 360°
Given,
Sum of the interior angles of a polygon
= 6.5...(Sum of the exterior angles of a polygon)
∴ (n - 2) x 180°
= 6.5 x 360°
⇒ n - 2 = 13
⇒ n = 15
∴ The polygon has 15 sides.
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