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The sum of the interior angles of a regular polygon is 2340°. What is the difference between an interior angle and an exterior angle of the polygon?

The sum of the interior angles of a regular polygon is 2340°. What is the difference between an interior angle and an exterior angle of the polygon? Correct Answer 132°

Given:

Sum of the interior angles of a regular polygon = 2340°

Formula used:

Sum of the interior angles of the polygon = (n - 2) × 180°

Sum of exterior angles of the polygon = 360°

Each Interior angle = / n

Each exterior angle = 360° / n

Calculation:

Sum of the interior angles of the polygon = (n - 2) × 180°

⇒ 2340 = (n - 2) × 180°

⇒ (n - 2) = 1340 / 180°

⇒ (n - 2) = 13

⇒ n = 13 + 2

⇒ n = 15

Each interior angle = 2340 / 15 = 156°

Each exterior angle = 360° / 15 = 24°

∴ Required difference = (156° - 24°) = 132°

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