# If the measure of one exterior angle of a regular polygon is 36 degrees, how many sides does the polygon have?

samhouston | Middle School Teacher | (Level 1) Associate Educator

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The sum of the exterior angles of any regular polygon is 360 degrees.

The exterior angles of a regular polygon are also equal.

Allow s to represent the number of sides of the polygon.

Therefore...

36s = 360

s = 10

Answer:  The polygon has 10 sides.

shaznl1 | High School Teacher | (Level 1) Salutatorian

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The sum of exterior angles of ANY regular polygon is 360 degrees

This can be proved because one exterior angle and one interior angle add up to be 180 degrees

the total interior angle sum is 180(n-2)

the total exterior +interior sum is 180n

180n-180(n-2)=360

In this question, each exterior angle is 36 degrees

the total is 360 degrees

Therefore, the number of sides is 360/36= 10 sides

It is a dodecagon

The polygon has 10 sides.

this method works for any regular polygon

giorgiana1976 | College Teacher | (Level 3) Valedictorian

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We'll recall that the number of sides of a regular polygon is equal to the number of exterior angles. We also know that the exterior angles of a regular polygon measure the same.

We know that the sum of all exterior angles of a polygon is of 360 degrees.

Let the number of exterior angles be n.

36 + 36 + ... + 36 = 360

n*36 = 360

n = 10

Since the number of exterior angles is equalt o the number of sides, then the regular polygon has 10 sides.