Question

question
what is the measure of each angle of a regular 17-gon? if necessary, round to the nearest tenth.
answer attempt 1 out of 2

Explanation:

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

The sum of the interior angles of a polygon with \( n \) sides is given by the formula \( S=(n - 2)\times180^{\circ} \). For a 17 - gon, \( n = 17 \). So we first calculate the sum of interior angles: \( S=(17 - 2)\times180^{\circ}=15\times180^{\circ} = 2700^{\circ} \).

Step2: Find the measure of each interior angle of a regular polygon.

In a regular polygon, all interior angles are equal. So the measure of each interior angle \( A \) is given by \( A=\frac{(n - 2)\times180^{\circ}}{n} \). Substituting \( n = 17 \) into the formula, we get \( A=\frac{2700^{\circ}}{17}\approx158.8^{\circ} \) (rounded to the nearest tenth).

Answer:

\( 158.8^{\circ} \)