Question

q.13 interior angles of polygons
what is the sum of the angle measures in this shape?

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides of the polygon.

Step2: Determine the number of sides of the polygon

The given polygon is a hexagon. A hexagon has \(n = 6\) sides.

Step3: Substitute \(n = 6\) into the formula

Substitute \(n=6\) into \(S=(n - 2)\times180^{\circ}\). Then \(S=(6 - 2)\times180^{\circ}\).
First, calculate \(6-2 = 4\). Then \(S=4\times180^{\circ}\).
Since \(4\times180^{\circ}=720^{\circ}\).

Answer:

\(720^{\circ}\)