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 find the measures of the angles of the parallelogram given that two adjacent angles are in the ratio of 3:2, we can follow these steps:

### Step 1: Assign Variables
Let the measures of the two adjacent angles be represented as:
- Angle A = 3x
- Angle B = 2x

### Step 2: Use the Property of Parallelograms
In a parallelogram, adjacent angles are supplementary, meaning they add up to 180 degrees. Therefore, we can write the equation:
\[ 3x + 2x = 180 \]

### Step 3: Simplify the Equation
Combine like terms:
\[ 5x = 180 \]

### Step 4: Solve for x
Now, divide both sides by 5 to find the value of x:
\[ x = \frac{180}{5} \]
\[ x = 36 \]

### Step 5: Find the Measures of the Angles
Now substitute the value of x back into the expressions for the angles:
- Angle A = 3x = 3(36) = 108 degrees
- Angle B = 2x = 2(36) = 72 degrees

### Step 6: List All Angles of the Parallelogram
In a parallelogram, opposite angles are equal. Therefore, the angles are:
- Angle A = 108 degrees
- Angle B = 72 degrees
- Angle C = 108 degrees (opposite to A)
- Angle D = 72 degrees (opposite to B)

### Final Answer
The measures of the angles of the parallelogram are:
- 108 degrees, 72 degrees, 108 degrees, and 72 degrees.

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