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 = 2n\times90^{circ} )
b. ( s=(n + 2)\times90^{circ} )
c. ( s=n\times180^{circ} )
d. ( s=(n - 2)\times180^{circ} ), then divide by n

Explanation:

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For a regular polygon (all angles equal), to find the measure of each interior angle, we divide the sum of interior angles by the number of sides \(n\). So we first use \(S=(n - 2)\times180^{\circ}\) to find the sum of interior angles and then divide by \(n\).

Answer:

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