If two adjacent angles of a parallelogram are in the ratio `2 : 3`, then the measure of angles are

Options

A. `72°, 108°`
B. `36°, 54° `
C. `80°, 120° `
D. `96°, 144°`

Answer

To solve the problem of finding the measures of two adjacent angles of a parallelogram that are in the ratio of 2:3, follow these steps:

### Step-by-Step Solution:

1. **Understand the properties of a parallelogram**: In a parallelogram, adjacent angles are supplementary, which means they add up to 180 degrees.

2. **Set up the ratio**: Let the two adjacent angles be represented as \(2x\) and \(3x\), where \(x\) is a common multiplier.

3. **Write the equation**: Since the angles are supplementary, we can write the equation:
\[ 2x + 3x = 180 \]

4. **Combine like terms**: Simplify the left side of the equation:
\[ 5x = 180 \]

5. **Solve for \(x\)**: Divide both sides by 5 to find the value of \(x\):
\[ x = \frac{180}{5} = 36 \]

6. **Calculate the angles**: Now substitute \(x\) back into the expressions for the angles:
- First angle:
\[ 2x = 2 \times 36 = 72 \text{ degrees} \]
- Second angle:
\[ 3x = 3 \times 36 = 108 \text{ degrees} \]

7. **Conclusion**: The measures of the two adjacent angles are \(72\) degrees and \(108\) degrees.

### Final Answer:
The measures of the angles are \(72\) degrees and \(108\) degrees.

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