Question

what is the measure of each interior angle of the regular polygon pictured below? if necessary, round to the nearest tenth.

Explanation:

Step1: Determine the number of sides

The polygon is labeled from 1 to 14, so it has \( n = 14 \) sides.

Step2: Use the formula for interior angles of a regular polygon

The formula for the measure of each interior angle of a regular polygon is \( \frac{(n - 2)\times180^\circ}{n} \). Substitute \( n = 14 \):
\[
\frac{(14 - 2)\times180^\circ}{14} = \frac{12\times180^\circ}{14}
\]

Step3: Calculate the value

First, calculate \( 12\times180 = 2160 \). Then divide by 14: \( \frac{2160}{14} \approx 154.3^\circ \) (rounded to the nearest tenth).

Answer:

\( 154.3^\circ \)