Question

The equation α = 180(n-2)/n represents the angle measures, α, in a regular n-sided polygon. When the equation is solved for n, n is equal to α fraction with a denominator of α - 180. What is the numerator of the fraction?

Answer 1

To solve for n in the given equation representing the angle measure of a regular n-sided polygon, the equation is manipulated algebraically resulting in the numerator of -360 for the solution expression of n.

Step-by-step explanation:

The student is asking for assistance in solving the equation α = 180(n-2)/n for n, which describes the measure of an interior angle (α) of a regular n-sided polygon. The solution involves algebraic manipulation of the equation to express n in terms of α.

First, we multiply both sides by n to get rid of the fraction: αn = 180(n - 2). Then we distribute the 180 on the right side: αn = 180n - 360. To solve for n, we rearrange terms to isolate n: αn - 180n = -360, and factor n out: n(α - 180) = -360.

Next, we divide both sides by (α - 180) to solve for n, which gives us n = -360/(α - 180). Hence, the numerator of the fraction for n is -360.