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If the measure of the interior angle of a regular polygon is 108° greater than the measure of its exterior angle then how many sides does it have?

If the measure of the interior angle of a regular polygon is 108° greater than the measure of its exterior angle then how many sides does it have? Correct Answer 10

For a regular polygon with ‘n’ sides,

Measure of exterior angle = 360°/n

Measure of interior angle = 180° - 360°/n

Let the no. of sides of the given polygon be ‘n’

Now,

Measure of interior angle - Measure of exterior angle = 108°

⇒ (180° - 360°/n) - (360°/n) = 108°

⇒ 180° - 720°/n = 108°

⇒ 180° - 108° = 720°/n

⇒ n = 720°/72°

⇒ n = 10

∴ No. of sides = 10

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