The measures of two adjacent angles of a parallelogram are in the ratio 3 : 2. Find the measure of each of the angles of the parallelogram.

Options

A. `72^@,108^@,72^@,108^@`
B. `62^@,108^@,62^@,108^@`
C. `72^@,118^@,72^@,118^@`
D. `70^@,108^@,70^@,108^@`

Explanation

To solve the problem, we need to find the measures of the angles of a parallelogram given that two adjacent angles are in the ratio of 3:2.

### Step-by-Step Solution:

1. **Understanding the Angles**:
In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Let's denote the two adjacent angles as \( \angle 1 \) and \( \angle 2 \).

2. **Setting Up the Ratio**:
According to the problem, the measures of the two adjacent angles are in the ratio 3:2. We can express these angles in terms of a variable \( x \):
- \( \angle 1 = 3x \)
- \( \angle 2 = 2x \)

3. **Using the Supplementary Angle Property**:
Since \( \angle 1 \) and \( \angle 2 \) are adjacent angles in a parallelogram, we can write the equation:
\[ \angle 1 + \angle 2 = 180^\circ \]
Substituting the expressions for the angles, we get:
\[ 3x + 2x = 180^\circ \]

4. **Solving for \( x \)**:
Combine the terms on the left side:
\[ 5x = 180^\circ \]
Now, divide both sides by 5:
\[ x = \frac{180^\circ}{5} = 36^\circ \]

5. **Finding the Angles**:
Now that we have the value of \( x \), we can find the measures of \( \angle 1 \) and \( \angle 2 \):
- \( \angle 1 = 3x = 3 \times 36^\circ = 108^\circ \)
- \( \angle 2 = 2x = 2 \times 36^\circ = 72^\circ \)

6. **Finding the Remaining Angles**:
In a parallelogram, opposite angles are equal. Therefore:
- \( \angle 3 = \angle 1 = 108^\circ \)
- \( \angle 4 = \angle 2 = 72^\circ \)

7. **Final Angles of the Parallelogram**:
The measures of the angles of the parallelogram are:
- \( \angle 1 = 108^\circ \)
- \( \angle 2 = 72^\circ \)
- \( \angle 3 = 108^\circ \)
- \( \angle 4 = 72^\circ \)

### Summary:
The measures of the angles of the parallelogram are \( 108^\circ, 72^\circ, 108^\circ, 72^\circ \).