Question

to calculate the measure of an angle in a regular polygon with 12 sides (a dodecagon), what formula would you use?
a. $s = 2n\times90^{circ}$
b. $s=(n - 2)\times180^{circ}$, then divide by $n$
c. $s = n\times180^{circ}$
d. $s=(n + 2)\times90^{circ}$

Explanation:

Step1: Recall the formula for the sum of interior angles

The sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides.

Step2: Find the measure of one interior angle in a regular polygon

Since a regular polygon has all angles equal, we divide the sum of interior angles by \(n\). So the formula for one interior angle is \(\frac{(n - 2)\times180^{\circ}}{n}\)

Answer:

B. \(S=(n - 2)\times180^{\circ}\), then divide by \(n\)