Question

12 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 the number of sides

The given polygon is a non - agon (9 - sided polygon), so \(n = 9\).

Step2: Apply the Polygon Angle Sum Theorem

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\).
Substitute \(n = 9\) into the formula:
\(S=(9 - 2)\times180^{\circ}\)
\(S = 7\times180^{\circ}\)
\(S=1260^{\circ}\)

Answer:

\(n = 9\), Sum of interior angles \(= 1260\) degrees.