Question

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

Explanation:

Step1: Recall polygon - sum formula

The sum of interior angles of a polygon is given by $(n - 2)\times180^{\circ}$, where $n$ is the number of sides. For a pentagon, $n = 5$. So, $(5 - 2)\times180^{\circ}=3\times180^{\circ}=540^{\circ}$.

Step2: Divide by number of angles

Since a regular pentagon has 5 equal - measure interior angles, we divide the sum of interior angles by 5. Let the measure of each interior angle be $z$. Then $z=\frac{(5 - 2)\times180^{\circ}}{5}=\frac{540^{\circ}}{5}=108^{\circ}$.

Answer:

$108^{\circ}$