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 of the polygon

The given polygon is a quadrilateral, so \(n = 4\).

Step2: Use the formula for the sum of interior angles of a polygon

The formula is \((n - 2)\times180^{\circ}\). Substitute \(n = 4\) into the formula: \((4 - 2)\times180^{\circ}\).

Step3: Calculate the result

\((4 - 2)\times180^{\circ}=2\times180^{\circ} = 360^{\circ}\)

Answer:

\(360^{\circ}\)