Interior and Exterior Angle of a Polygon: Formula not working

[zak100]

Homework Statement

How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle?

Homework Equations

Interior angle of a polygon: ((n-2) * 180)/n
Exterior angle of a polygon: (360)/n

The Attempt at a Solution

((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 is the problem.

Zulfi.

 

[Mark44]

Homework Statement

How many sides does a polygon have if the measure of each interior angle is 8 times the measure of each exterior angle?

Homework Equations

Interior angle of a polygon: ((n-2) * 180)/n
Exterior angle of a polygon: (360)/n

The Attempt at a Solution

((n-2) * 180)/n = 8 * (360)/n
now ((n-2) * 180) = 8 * 360
180 n -360 = 8 * 360

Work is fine to here, but you have a mistake in the line below. Two lines above, it would be simpler to divide both sides by 180, to get simpler numbers to work with.
Alternatively, in the line above, you are adding 360 to both sides of the equation.

180 n = 7 * 360
n = 14
I am getting n = 14 which is wrong.

Some body please guide me what is the problem.

Zulfi.

 

[QuantumQuest]

180 n -360 = 8 * 360
180 n = 7 * 360

Check the math

EDIT: beaten for some seconds by Mark44

 

[zak100]

Hi,
Thanks. I found my mistake.

180 n -360 = 8 * 360

Reference https://www.physicsforums.com/threa...ngle-of-a-polygon-formula-not-working.933140/

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

This is correct.

Thanks.
Zulfi.