Question

1. to calculate the measure of an angle in a regular polygon with 12 sides (a dodecagon), what formula would you use?

a. $s = n×180^{circ}$

b. $s = 2n×90^{circ}$

c. $s=(n + 2)×90^{circ}$

d. $s=(n - 2)×180^{circ}$, then divide by $n$

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

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

Step2: Recall the formula for the measure of each interior angle of a regular polygon

For a regular polygon (all angles equal), the measure of each interior angle is \(\frac{(n - 2)\times180^{\circ}}{n}\), which is obtained by first finding the sum of interior angles \(S=(n - 2)\times180^{\circ}\) (from Step1) and then dividing by the number of sides \(n\).

Answer:

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