Question

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explain how the triangulated polygon relates to the formula for the measure of the interior angles of a polygon.
the figure shows that the polygon, which has
measure of
180°
360°
therefore, the total measure of the interior angles of this polygon is
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Explanation:

Step1: Count the number of sides

The given polygon is a hexagon, which has \(6\) sides.

Step2: Determine the number of triangles

A polygon with \(n\) sides can be divided into \((n - 2)\) triangles. For \(n=6\), \(6- 2=4\) triangles.

Step3: Use the sum of interior angles of a triangle

The sum of interior angles of a triangle is \(180^{\circ}\).

Step4: Calculate the sum of interior angles of the polygon

If there are \(k\) triangles, the sum of interior angles of the polygon is \(k\times180^{\circ}\). Here \(k = 4\), so \(4\times180^{\circ}=720^{\circ}\)

Answer:

The polygon has \(6\) sides, may be divided into \(4\) triangles, each with a total interior - angle measure of \(180^{\circ}\). So the total measure of the interior angles of this polygon is \(720^{\circ}\).