Solution:

Let's assume that the angles of the pentagon are 5x, 4x, 3x, 6x, and 2x.

The sum of the interior angles of a pentagon is 180°(n-2), where n is the number of sides of the polygon.

Therefore, the sum of the interior angles of the pentagon is:

180°(5-2) = 540°

We can use this information to create an equation involving the ratio of the angles:

5x + 4x + 3x + 6x + 2x = 540°

Simplifying this equation, we get:

20x = 540°

x = 27°

Now we can find the measure of each angle by substituting x = 27° into our original assumption:

- The first angle is 5x = 5(27°) = 135°
- The second angle is 4x = 4(27°) = 108°
- The third angle is 3x = 3(27°) = 81°
- The fourth angle is 6x = 6(27°) = 162°
- The fifth angle is 2x = 2(27°) = 54°

Therefore, the measure of each angle in the pentagon is:

- 135°
- 108°
- 81°
- 162°
- 54°

Summary:

- Let the angles of the pentagon be 5x, 4x, 3x, 6x, and 2x.
- The sum of the interior angles of a pentagon is 180°(n-2), where n is the number of sides of the polygon.
- Using the sum of the interior angles of the pentagon, we can create an equation involving the ratio of the angles.
- By solving for x, we can find the measure of each angle.
- The measure of each angle in the pentagon is 135°, 108°, 81°, 162°, and 54°.

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