Question

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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.

Explanation:

Step1: Triangle angle sum

The sum of interior angles of any triangle is a constant value:
$$180$$

Step2: Equilateral triangle interior angle

Divide the total sum by 3 equal angles:
$$\frac{180}{3} = 60$$

Step3: Hexagon triangle count

A regular hexagon can be divided into 4 equilateral triangles from its center.

Step4: Hexagon total interior angles

Multiply triangle count by triangle angle sum:
$$4 \times 180 = 720$$

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.