Question

question
what is the sum of 9 of the interior angles of a regular dodecagon?
answer attempt 1 out of 2
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Explanation:

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

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \). A dodecagon has \( n = 12 \) sides.

Step2: Calculate the sum of all interior angles of a dodecagon

Substitute \( n = 12 \) into the formula: \( S=(12 - 2)\times180^{\circ}=10\times180^{\circ} = 1800^{\circ} \).

Step3: Find the measure of one interior angle of a regular dodecagon

Since a regular dodecagon has all interior angles equal, the measure of one interior angle \( \theta=\frac{1800^{\circ}}{12}=150^{\circ} \).

Step4: Calculate the sum of 9 interior angles

Multiply the measure of one interior angle by 9: \( 9\times150^{\circ}=1350^{\circ} \).

Answer:

\( 1350 \)