If each interior angle of a polygon is 108 degree find number of sides.Also write the name of that polygon.

Answers (1)

If n is the number of sides, each interior angle I can be calculated by the following formula:

I = 180(n - 2)/n

Substitute:

108 = 180(n - 2)/n

Multiply both sides by n:

108n = 180(n - 2)

Distribute:

108n = 180n - 360

Subtract 180n from both sides:

108n - 180n = -360

Combine like terms:

-72n = -360

Divide both sides by -72:

n = 5

Its a pentagon

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