The measure of each interior angle of a regular polygon with n sides is [(n - 2)180 / n] degrees. What is the measure of each interior angle of a regular polygon with n sides, in radians?
A. (n - 2)pi / 4n
B. (n - 2)pi / 2n
C. (n - 2)pi / n
D. (n - 2)2pi / n
E. (n - 2)4pi / n
Measure of each interior angle
=(N-2)(180)_n
To find the measure of each interior angle of a regular polygon with n sides in radians, we need to convert the formula given in degrees into radians.
1. Start with the formula: (n - 2)180 / n degrees.
2. To convert degrees to radians, we need to multiply by the conversion factor (pi / 180).
3. Multiply the formula by (pi / 180): [(n - 2)180 / n] * (pi / 180).
4. Simplify the expression: [(n - 2)pi / n].
So, the measure of each interior angle of a regular polygon with n sides, in radians, is (n - 2)pi / n.
Therefore, the answer is C. (n - 2)pi / n.
To convert from degrees to radians, you can use the conversion factor:
1 radian = 180 degrees / π
First, let's substitute the given formula for the measure of each interior angle in degrees into radians using the conversion factor:
Measure of each interior angle in radians = [(n - 2)180 / n] * (1 radian / 180 degrees)
Measure of each interior angle in radians = [(n - 2) / n] * π radians
Now, let's simplify the expression:
Measure of each interior angle in radians = [(n - 2) / n] * π
Measure of each interior angle in radians = (n - 2)π / n
Comparing this result to the given choices, we can see that the correct answer is:
C. (n - 2)π / n