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.zak100 said: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
zak100 said:180 n = 7 * 360
n = 14
I am getting n = 14 which is wrong.
Some body please guide me what is the problem.
Zulfi.
zak100 said:180 n -360 = 8 * 360
180 n = 7 * 360
The formula for finding the interior angle of a regular polygon is (n-2) x 180 / n, where n is the number of sides. The formula for finding the exterior angle of a regular polygon is 360 / n.
The formula only works for regular polygons, meaning all sides and angles are equal. If your polygon is irregular, the formula will not apply and you will need to use a different method to find the interior and exterior angles.
No, the formula is only applicable for regular polygons. For irregular polygons, the sum of the interior angles can still be found using the formula (n-2) x 180, but individual angles cannot be determined using this formula.
If you know the number of sides of a regular polygon, you can use the formulas mentioned in the first question to find the interior and exterior angles.
Yes, there are other methods such as using trigonometry or dividing the polygon into triangles. These methods can be used for both regular and irregular polygons.