Question

approximately how many degrees are in the measure of an interior angle of a regular eight sided polygon?
135
45
180
225

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 regular octagon, \( n = 8 \).

Step2: Calculate the sum of interior angles

Substitute \( n = 8 \) into the formula: \( S=(8 - 2)\times180^{\circ}=6\times180^{\circ} = 1080^{\circ} \).

Step3: Calculate the measure of one interior angle

In a regular polygon, all interior angles are equal. So, the measure of one interior angle \( \theta=\frac{S}{n} \). Substitute \( S = 1080^{\circ} \) and \( n = 8 \): \( \theta=\frac{1080^{\circ}}{8}=135^{\circ} \).

Answer:

135 (corresponding to the option "135")