If two complementary angles are in the ratio 13 : 5, then the angles are:

Answer

To solve the problem of finding two complementary angles that are in the ratio of 13:5, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Complementary Angles**:
Complementary angles are two angles whose sum is 90 degrees.

2. **Set Up the Angles Based on the Ratio**:
Let the two angles be represented as:
- First angle = \( 13x \)
- Second angle = \( 5x \)

3. **Write the Equation for Complementary Angles**:
Since the angles are complementary, we can write the equation:
\[ 13x + 5x = 90 \]

4. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 18x = 90 \]

5. **Solve for \( x \)**:
To find the value of \( x \), divide both sides of the equation by 18:
\[ x = \frac{90}{18} = 5 \]

6. **Find the Angles**:
Now that we have the value of \( x \), we can find the measures of the angles:
- First angle:
\[ 13x = 13 \times 5 = 65 \text{ degrees} \]
- Second angle:
\[ 5x = 5 \times 5 = 25 \text{ degrees} \]

7. **State the Final Answer**:
Therefore, the two complementary angles are:
- \( 65 \) degrees and \( 25 \) degrees.

### Final Answer:
The two complementary angles are \( 65 \) degrees and \( 25 \) degrees.

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