Solve for n
á = (n-2) * 180 / n = 180 – 360/n
Although you do not need to know this to answer that question, that is the formula for each internal angle (a) of a regular polygon with n sides.
360/n = 180-a
n = 360/(180-a)
n = 4 for a = 90 degrees (a square) etc.
To solve for n in the equation á = (n-2) * 180 / n = 180 – 360/n, we need to simplify the equation and isolate the variable.
Let's start by simplifying the equation step by step:
1. Remove the common denominator by multiplying both sides of the equation by n:
n * á = (n-2) * 180 = 180n - 360
2. Distribute 180 to both terms inside the parentheses on the right side:
n * á = 180n - 360
3. Move all terms to one side of the equation:
n * á - 180n = -360
4. Combine like terms:
n(á - 180) = -360
To solve for n, we will divide both sides of the equation by (á - 180):
n = -360 / (á - 180)
Now you can substitute the given value of á into this equation to find the value of n.