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The sum of interior angle of a regular polygon is 1800°. What is the difference between an interior and an exterior angle of the regular polygon?

The sum of interior angle of a regular polygon is 1800°. What is the difference between an interior and an exterior angle of the regular polygon? Correct Answer 120

Given:

The sum of an interior angle of the regular polygon is 1800° 

Concept used:

Sum of an interior angle of regular polygon = (n - 2) × 180° 

An exterior angle of the polygon = 360°/n

Where n is the number of sides in the polygon

Calculation:

Sum of an interior angle of regular polygon = (n - 2) × 180° 

According to the question

⇒ 1800° = (n - 2)180° 

⇒ n = 12

The number of sides in a regular polygon is 12

An exterior angle of the polygon = 360°/n

⇒ An exterior angle = 360°/12 = 30° 

we know the sum of an exterior and an interior angle of the regular polygon is 180

⇒ An interior angle of polygon = 180° - 30° = 150° 

The difference between an interior and an exterior angle of the regular polygon = 150° - 30° 

⇒ 120° 

∴ The difference between an interior and an exterior angle of the regular polygon120° 

 

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