The measures of two consecutive angles of a parallelogram are in the Ratio 3:7. Find the measure of an acute angle of the parallelogram

Let's denote the two consecutive angles of the parallelogram as 3x and 7x, where x is a positive integer.

In a parallelogram, consecutive angles are supplementary, which means they add up to 180 degrees.

Therefore, we can set up the equation:
3x + 7x = 180

Combining like terms, we get:
10x = 180

To isolate x, we divide both sides of the equation by 10:
x = 18

Now that we have the value of x, we can substitute it back into the expression for the acute angle, which is 3x:
3(18) = 54 degrees.

Therefore, the measure of an acute angle of the parallelogram is 54 degrees.

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

Let's assume the measures of the two consecutive angles are 3x and 7x, where x is a common factor.

In a parallelogram, the opposite angles are equal. Since the given angles are consecutive, they are opposite to each other.

Therefore, we can equate the measures of the two consecutive angles:

3x = 7x

To solve for x, we subtract 3x from both sides:

7x - 3x = 0

Simplifying, we get:

4x = 0

Dividing both sides by 4, we find:

x = 0

Since x = 0, it means that the two consecutive angles have a measure of 0 degrees.

However, since we are looking for an acute angle (which is less than 90 degrees) in the parallelogram, it seems that the information provided may not be accurate or it is not possible to determine the measure of the acute angle based on the given ratio.

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