Question

1. find the measure of z. regular octagon 108° 144° 120° 135°

Explanation:

Step1: Recall the formula for the interior angle of a regular polygon.

The formula for the measure of each interior angle of a regular polygon with \( n \) sides is \( \frac{(n - 2)\times180^{\circ}}{n} \).

Step2: Identify the number of sides of the polygon.

A regular octagon has \( n = 8 \) sides.

Step3: Substitute \( n = 8 \) into the formula.

Substitute \( n = 8 \) into \( \frac{(n - 2)\times180^{\circ}}{n} \):

$$ \frac{(8 - 2)\times180^{\circ}}{8} = \frac{6\times180^{\circ}}{8} $$

Step4: Calculate the value.

First, calculate \( 6\times180^{\circ}=1080^{\circ} \). Then, divide by 8: \( \frac{1080^{\circ}}{8} = 135^{\circ} \).

Answer:

\( 135^{\circ} \) (corresponding to the option with \( 135^{\circ} \))