The difference between interior andexteriorangleof a regular polygon is 100anddeg;. Find the numberof sides of polygon.a)7b)8c)9d)10Correct answer is option 'C'. Can you explain this answer?

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The difference between interior and exterior angle of a regular polygon is 100°. Find the number of sides of polygon.

a)
7
b)
8
c)
9
d)
10

Correct answer is option 'C'. Can you explain this answer?

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The difference between interior andexteriorangleof a regular polygon i...

Let out of exterior and interior angle one of the angle be x
∴ Other angle = x + 100.
Now as we know that interior angle + exterior angle = 180°
∴ x + x + 100 = 180°
⇒ 2x + 100 = 180°
⇒ 2x = 80°
⇒ x = 40°
∴ other angle = 140°
Now, since exterior angle of a regular polygon can not exceed 120°
∴ Interior angle = 140° and, Exterior angle = 40°
Now no. of sides of a regular polygon = 360 / exterior angle
∴ No. of sides = 360 / 40 = 9

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