The number of sides in a regular polygon

Question:

The number of sides in a regular polygon having measure of an exterior angle as 72o is __________.

Solution:

The number of sides in a regular polygon having measure of an exterior angle as 72o is 5.

We know that, the measure of each exterior angle of a regular pentagon is 360o/n.

Where ‘n’ is the number of sides in the polygon,

Then, pentagon has exterior angle = 72o

So, 72o = 360o/n

n = 360o/72o

n = 5

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