The measures of two consecutive angles of a parallelogram are in the ratio 6: 3. what is the measure of an acute angle of the parallelogram?

The measure of an acute angle of the parallelogram is .

Step-by-step explanation:

As we know by the property of parallelogram :

Consecutive angles of a parallelogram are supplementary.

Given: The measure of two consecutive angles of a parallelogram are in the ratio 6: 3.

Then;

6x be the measure of larger angle and 3x be the measure of smaller angle.

⇒  

Combine like terms;

Divide both sides by 9 we get;

Simplify:

Then, the measure of larger angle 6x = and

the measure of smaller angle 3x = .

Since, we know that in a parallelogram, opposite interior angles are equal.

Acute angle is an angle smaller than a right angle(i.e 90 degree)

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