# Interior and Exterior Angle of a Polygon: Formula not working

#### zulfi100

Joined Jun 7, 2012
656
Hi,
I have got following question:
How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle?

The formula to find measurement of each interior angle of a polygon is:
((n-2) * 180)/n and the formula to find the measurement of each exterior angle is:
360/n

Now ((n-2) * 180)/n = 8 * (360)/n
now ((n-2) * 180) = 8 * 360
180 n -360 = 8 * 360
180 n = 7 * 360
n = 14
I am getting n = 14 which is wrong.

Some body please guide me what's the prob with it.

Zulfi.

#### MrAl

Joined Jun 17, 2014
11,494
Hi,

Did you check your formulas online somewhere?
I ask because for a square (4 sides) the interior angles are:
ang=360/4=90 degrees each.

#### zulfi100

Joined Jun 7, 2012
656
Hi,
My friend thanks. Its saying polygon so i used the formula of polygon from the book.

Zulfi.

#### zulfi100

Joined Jun 7, 2012
656
Hi,
I found my mistake in the calculation:

It should be.
180 n -360 = 8 * 360
180 n = 9 * 360
Therefore, n= 18.

This is correct.

Thanks.
Zulfi.

#### MrAl

Joined Jun 17, 2014
11,494
Hi,
My friend thanks. Its saying polygon so i used the formula of polygon from the book.

Zulfi.
Hi,

Ok then next check your math itself. I get a number larger than 14.

EDIT:
Ok you found it good

I had to look up the formulas too to make sure they were right.

#### WBahn

Joined Mar 31, 2012
30,074
You should also be able to figure it out without looking up any formulas at all, provided you understand some simple basics about angles.

You spend too much of your time chasing down formulas and too little time thinking about the problem in order to understand the concepts. The result is that, the next time you are faced with a similar problem, you have to start all over and chase down someone else's formulas because you don't understand the concepts well enough to solve the problem on your own.
You know that the interior and exterior angles must add to 180° (since they are supplementary angles). So if A is the exterior angle, then you have

8A + A = 180°
9A = 180°
A = 20°

You also know that at each vertex your path changes course by the amount of the exterior angle and that, after all N vertices, you have to be going in the same direction again, so

N·A = 360°

N = 360°/A = 360°/20° = 18