Question

what is the sum of 11 of the interior angles of a regular dodecagon?

answer attempt 1 out of 2

Explanation:

Step1: Find sum of interior angles of dodecagon

A dodecagon has \( n = 12 \) sides. The formula for the sum of interior angles of a polygon is \( (n - 2)\times180^{\circ} \). Substituting \( n = 12 \), we get \( (12 - 2)\times180^{\circ}=10\times180^{\circ} = 1800^{\circ} \).

Step2: Find measure of one interior angle

In a regular dodecagon, all interior angles are equal. So one interior angle is \( \frac{1800^{\circ}}{12}=150^{\circ} \).

Step3: Find sum of 11 interior angles

Multiply the measure of one interior angle by 11: \( 11\times150^{\circ}=1650^{\circ} \).

Answer:

\( 1650^{\circ} \)