Question

1. find the missing angle of the polygon.

Explanation:

Step1: Recall sum - of - interior - angles formula

The sum of interior angles of an $n$-sided polygon is given by $(n - 2)\times180^{\circ}$. Here, $n=8$, so the sum is $(8 - 2)\times180^{\circ}= 1080^{\circ}$.

Step2: Sum the known angles

$95^{\circ}+170^{\circ}+155^{\circ}+115^{\circ}+z + 125^{\circ}+110^{\circ}+95^{\circ}=865^{\circ}+z$.

Step3: Solve for the missing angle

Set the sum of known angles equal to the total sum of interior angles and solve for $z$.
$865^{\circ}+z=1080^{\circ}$, so $z = 1080^{\circ}-865^{\circ}=215^{\circ}$.

Answer:

$215^{\circ}$