The measures of two consecutive angles of a parallelogram are in the ratio 5:4. What is the measure of an acute angle of the parallelogram?

since consecutive angles are supplementary,

5x+4x=180
x = 20
The angles are 80° and 100°

To determine the measure of an acute angle of the parallelogram, we need to find the measures of the consecutive angles.

Let's assume that one of the angles is represented by 5x, where x is a scaling factor. And the other angle is represented by 4x.

Since the consecutive angles of a parallelogram are supplementary (their sum is 180 degrees), we can set up the following equation:

5x + 4x = 180

Combining like terms, we get:

9x = 180

To isolate x, we divide both sides of the equation by 9:

x = 20

Now, we can substitute the value of x back into 5x or 4x to find the measure of one of the angles:

5x = 5 * 20 = 100 degrees

So, the measure of one of the angles is 100 degrees. Since the opposite angles of a parallelogram are congruent, the measure of the other acute angle will also be 100 degrees.