Question

question
what is the measure of each angle of a regular 22 - gon? if necessary, round to the nearest tenth.
answer attempt 2 out of 2

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 \( S=(n - 2)\times180^{\circ} \). For a 22 - gon, \( n = 22 \).
So, we first calculate the sum of interior angles: \( S=(22 - 2)\times180^{\circ}=20\times180^{\circ} = 3600^{\circ} \)

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 \( A=\frac{(n - 2)\times180^{\circ}}{n} \)
Substitute \( n = 22 \) into the formula: \( A=\frac{(22 - 2)\times180^{\circ}}{22}=\frac{3600^{\circ}}{22}\approx163.6^{\circ} \)

Answer:

\( 163.6^{\circ} \)