regular hexagon abcdef is divided into six equilateral triangles, as shown. explain how to determine the sum…

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 choose... degrees.

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 choose... degrees.

Answer

Explanation:

Step1: Recall triangle angle - sum

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

Step2: Angle of equilateral triangle

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

Step3: Hexagon - triangle relation

At each vertex of the regular hexagon, 2 interior angles of equilateral triangles meet.

Step4: Calculate hexagon interior - angle sum

The hexagon is divided into 6 triangles. The sum of the interior angles of the hexagon is the sum of the interior angles of these 6 triangles. So the sum is $6\times180 - 360=720$ degrees (we subtract 360 degrees because the angles at the center that are not part of the hexagon's interior angles sum to 360 degrees). Another way is to note that since there are 6 vertices and each vertex - angle of the hexagon is composed of 2 angles of 60 - degree equilateral - triangle angles, the sum of interior angles of the hexagon is $720$ 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.