Question

the diagram shows a convex polygon. what is the sum of the interior angle measures of this polygon?

Explanation:

Step1: Identify the number of sides

The polygon is a \(10 -\)sided polygon (\(n = 10\)).

Step2: Use the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is \((n - 2)\times180^{\circ}\). Substitute \(n = 10\) into the formula: \((10 - 2)\times180^{\circ}=8\times180^{\circ}\).

Step3: Calculate the result

\(8\times180^{\circ}=1440^{\circ}\)

Answer:

\(1440^{\circ}\)