Question

regular hexagon abcdef is divided into six equilateral triangles, as shown. explain how to determine the sum of the interior angles of the hexagon using these triangles. use the drop - down menus to complete the statements. click the arrows to choose an answer from each menu. the sum of the interior angles of each triangle is choose... degrees, so the measure of each interior angle of the equilateral triangles in the figure is choose... degrees. the interior angle at each vertex of the hexagon is composed of choose... interior angles of an equilateral triangle. so, the sum of the interior angles of the regular hexagon is degrees.

Explanation:

Step1: Recall triangle angle - sum property

The sum of the interior angles of any triangle is 180 degrees.

Step2: Find angle of equilateral triangle

In an equilateral triangle, all interior angles are equal. So, each interior angle is $\frac{180}{3}=60$ degrees.

Step3: Analyze hexagon - triangle relation

Each vertex of the regular hexagon is composed of 2 interior angles of an equilateral triangle.

Step4: Calculate sum of hexagon interior angles

The hexagon has 6 vertices. Each vertex contributes 2 angles of 60 degrees. So the sum of the interior angles of the hexagon is $6\times120 = 720$ degrees.

Answer:

The sum of the interior angles of each triangle is 180 degrees, so the measure of each interior angle of the equilateral triangles in the figure is 60 degrees. The interior angle at each vertex of the hexagon is composed of 2 interior angles of an equilateral triangle, so the sum of the interior angles of the regular hexagon is 720 degrees.