In adjacent sides of a parallelogram, two lines are parallel and one is transversal.
Assume AB parallel to CD and BC is the transversal.
So, angle ABC + angle BCD = 180 deg. ( co int angles )
let the ratio be x
2x + 3x = 180
5x = 180
x = 180/5
= 36
2x= 2*36= 72
3x= 3*36 = 108

The adjacent angles in a parallelogram are supplementary, which means that their measures add up to 180 degrees. Let's assume that the smaller angle has a measure of 2x degrees, and the larger angle has a measure of 3x degrees.

To find the value of x and subsequently the measures of the angles, we can set up an equation based on the fact that the sum of the measures of adjacent angles in a parallelogram is 180 degrees.

Step 1: Set up the equation:
2x + 3x = 180

Step 2: Combine like terms:
5x = 180

Step 3: Solve for x by dividing both sides of the equation by 5:
x = 36

Step 4: Substitute the value of x back into the expressions for the angles to find their measures:
Angle 1: 2x = 2 * 36 = 72 degrees
Angle 2: 3x = 3 * 36 = 108 degrees

Therefore, the measures of the adjacent angles in the parallelogram are 72 degrees and 108 degrees.

Summary:
- The adjacent angles in a parallelogram are supplementary.
- We can set up an equation based on the sum of the measures of adjacent angles in a parallelogram.
- By solving the equation, we can find the value of x.
- Substituting x back into the expressions for the angles gives their measures.
- In this case, the measures of the adjacent angles are 72 degrees and 108 degrees.