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If the measure of one exterior angle of a regular polygon is 40 degrees, how many sides does the polygon have?

Answer 1

The polygon has 9 sides

Explanation:

we know that

A regular polygon has equal length sides and equal interior angles

step 1

Find the measure of the interior angle

Remember that

The interior angle plus the exterior angle must be equal to 180 degrees (form a linear pair)

Let

x ----> the measure of each interior angle in the regular polygon

so

`x+40^o=180^o`

solve for x

`x=180^o-40^o=140^o`

step 2

Find the number of sides of the regular polygon

we know that

The measure of each interior angle in a regular polygon is given by the formula

`x=((n-2)180^o)/(n)`

where

n is the number of sides of the polygon

substitute the given values

`140^o=((n-2)180^o)/(n)`

solve for n

`140n=180n-360\\180n-140n=360\\40n=360\\n=9\ sides`

therefore

The polygon has 9 sides