The two back legs of the directors chair meet in a 72 degree angle. Find the measure of each angle formed by the two back legs.

To find the measure of each angle formed by the two back legs of the director's chair, we can start by recognizing that the sum of the interior angles of a triangle is 180 degrees. Since the two back legs form a straight line, they can be considered as one of the sides of a triangle.

Let's assume that the angle formed by one back leg with the horizontal is x degrees. Since we are given that the two back legs meet at a 72 degree angle, the angle formed by the other back leg with the horizontal would be (180 - 72) = 108 degrees.

Now, let's consider the triangle formed by one back leg, the horizontal, and the other back leg. The sum of the interior angles of this triangle should also be equal to 180 degrees.

The angles in the triangle can be represented as follows:
- The angle formed by one back leg with the horizontal = x degrees.
- The angle formed by the other back leg with the horizontal = 108 degrees.
- The remaining angle in the triangle = 180 - (108 + x) = 72 - x degrees.

Since we know that the sum of the angles in a triangle is equal to 180 degrees, we can write the equation:
x + 108 + (72 - x) = 180

Simplifying this equation:
x + 108 + 72 - x = 180
180 + 180 = 180

The equation simplifies to:
180 = 180

This equation holds true, which means that any value of x will satisfy it. Therefore, the measure of each angle formed by the two back legs of the director's chair can vary.