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 has 12 sides (as labeled from 1 to 12). For a regular polygon with \( n \) sides, the formula for the sum of interior angles is \( (n - 2)\times180^\circ \). Here, \( n = 12 \).

Step2: Calculate the sum of interior angles

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

Step3: Find the measure of one interior angle

Since it's a regular polygon, all interior angles are equal. So divide the sum by the number of sides: \( \frac{1800^\circ}{12}=150^\circ \).

Answer:

\( 150 \)