Question

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

Explanation:

Step1: Determine the number of sides (n)

The diagram shows a regular octagon, which has 8 sides. So, \( n = 8 \).

Step2: Apply the Polygon Angle Sum Theorem

The Polygon Angle Sum Theorem states that the sum of the interior angles of a polygon with \( n \) sides is given by the formula \( S=(n - 2)\times180^{\circ} \).
Substitute \( n = 8 \) into the formula:
\( S=(8 - 2)\times180^{\circ} \)
\( S = 6\times180^{\circ} \)
\( S = 1080^{\circ} \)

Answer:

\( n = 8 \)
Sum of Interior Angles \( = 1080 \) degrees.