Question

select the correct answer from each drop - down menu. 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 sides, may be divided into triangles, each of which will have a total interior angle measure of. therefore, the total measure of the interior angles of this polygon is.

Explanation:

Step1: Identify polygon sides

Count the sides of the polygon: A, B, C, D, E, F → 6 sides.

Step2: Count formed triangles

From vertex F, the polygon is split into $\triangle FAB$, $\triangle FBC$, $\triangle FCD$, $\triangle FDE$ → 4 triangles.

Step3: Recall triangle interior sum

The total interior angle measure of one triangle is $180^\circ$.

Step4: Calculate polygon interior sum

Multiply number of triangles by $180^\circ$: $4 \times 180^\circ = 720^\circ$

Answer:

The figure shows that the polygon, which has 6 sides, may be divided into 4 triangles, each of which will have a total interior angle measure of $180^\circ$. Therefore, the total measure of the interior angles of this polygon is $720^\circ$.