Question

Erks 3 HC Vans Surf Boots H... SD-Algebra 1 (Arbis Blended) The equation a = 180(n-2) n represents the angle measures, a, in a regular n-sided polygon. When the equation is solved for n, n is equal to a fraction with a denominator of a - 180. What is the numerator of the fraction?

A. 180
B. a
C. a - 180
D. a + 180

Answer 1

When solving the equation a = 180(n - 2) for n, we rearrange the terms to find n = (a + 360)/(a - 180), where the numerator of this fraction is a + 360.

Step-by-step explanation:

The equation given is a = 180(n - 2), which represents the angle measures (a) in a regular n-sided polygon. We need to solve this equation for n to express it in the form of a fraction with a denominator of a - 180. To solve for n, we would arrange the terms as follows:

a = 180(n - 2)

a/180 = n - 2

n = (a/180) + 2

Next, to make the denominator a - 180, we can multiply numerator and denominator by the same value, resulting in:

n = ((a/180) + 2) * ((a - 180)/(a - 180))

n = (a + 360)/(a - 180)

The numerator of the fraction that represents n will then be a + 360.