Question

for the diagram, determine the number of sides use the polygon angle sum theorem to find the sum of the interior angles: (show all work on paper) n = sum of interior angles = degrees.

Explanation:

Step1: Count number of sides

The polygon is an octagon, so $n = 8$.

Step2: Apply polygon - angle sum formula

The formula for the sum of interior angles of a polygon is $(n - 2)\times180^{\circ}$. Substitute $n = 8$ into the formula: $(8 - 2)\times180^{\circ}=6\times180^{\circ} = 1080^{\circ}$.

Answer:

$n = 8$
Sum of Interior Angles $= 1080$ degrees.