# The measure of an interior angle of a regular polygon is 160. How many sides does the polygon have?

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20
Jan 3, 2016

18

#### Explanation:

There are more complicated ways to do this, but I've always found this to be the easiest/fastest way. The Exterior angles of a polygon always add up to 360 degrees (they make their way all the way around the polygon...full circle).

The interior angle and the exterior angle add up to 180 degrees since they form a straight line.

Your interior angle was 160 degrees so the exterior angle would be 20 degrees. Now that we know an exterior angle we can divide to find out how many there are.

360 degrees divided by 20 degrees = 18 sides

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15
gole s. Share
Nov 15, 2016

ANS= 18 as mentioned before

#### Explanation:

the following formula is going to used
interior angle(int)=$\frac{n - 2}{2} \cdot 360$
where;n= number of sides.
just substitute values and find n which will be n=18.
THANK YOU

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sjc Share
Jul 9, 2017

$18 \text{ sides }$

#### Explanation:

with regular polygons it is best to remember that:

$\left(1\right) \text{ }$all the EXTERIOR angles add up to ${360}^{0}$

$\left(2\right) \text{ }$ $1 \text{ exterior angle"+ 1" interior angle } = {180}^{0}$

Work with the exterior angles. In this case:

$1 \text{ int. <} = 180 - 160 = {20}^{0}$

$\text{No. of sides } = \frac{360}{20} = 18$

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