Two adjacent angles on a straight line are in the ratio 5 : 4. find the measure of each one of these angles.

Options

A. `100^(@), 90^(@)`
B. `90^(@), 90^(@)`
C. `100^(@), 80^(@)`
D. `70^(@), 80^(@)`

Explanation

To solve the problem of finding the measures of two adjacent angles on a straight line that are in the ratio of 5:4, follow these steps:

### Step-by-Step Solution:

1. **Understand the problem**: We have two adjacent angles on a straight line, which means they add up to 180 degrees. The angles are in the ratio of 5:4.

2. **Assign variables**: Let the first angle be \(5x\) and the second angle be \(4x\), where \(x\) is a common multiplier.

3. **Set up the equation**: Since the angles are adjacent and form a straight line, we can write the equation:
\[ 5x + 4x = 180 \]

4. **Combine like terms**: This simplifies to:
\[ 9x = 180 \]

5. **Solve for \(x\)**: Divide both sides by 9:
\[ x = \frac{180}{9} = 20 \]

6. **Find the angles**: Now, substitute \(x\) back into the expressions for the angles:
- First angle:
\[ 5x = 5 \times 20 = 100 \text{ degrees} \]
- Second angle:
\[ 4x = 4 \times 20 = 80 \text{ degrees} \]

7. **Conclusion**: The measures of the two angles are:
- First angle: \(100\) degrees
- Second angle: \(80\) degrees

### Final Answer:
- The two adjacent angles are \(100\) degrees and \(80\) degrees.

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