Two complementry angle differby `14^(@)` the larger angle is

Answer

To solve the problem of finding the larger angle when two complementary angles differ by 14 degrees, we can follow these steps:

### Step-by-Step Solution:

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

2. **Define the Angles**:
Let one angle be \( x \). Since the two angles differ by 14 degrees, the other angle can be expressed as \( x + 14 \).

3. **Set Up the Equation**:
Since the angles are complementary, we can set up the equation:
\[ x + (x + 14) = 90 \]

4. **Combine Like Terms**:
Combine the terms on the left side:
\[ 2x + 14 = 90 \]

5. **Isolate the Variable**:
Subtract 14 from both sides to isolate the term with \( x \):
\[ 2x = 90 - 14 \]
\[ 2x = 76 \]

6. **Solve for \( x \)**:
Divide both sides by 2 to find the value of \( x \):
\[ x = \frac{76}{2} = 38 \]

7. **Find the Other Angle**:
Now, substitute \( x \) back to find the other angle:
\[ x + 14 = 38 + 14 = 52 \]

8. **Identify the Larger Angle**:
The two angles are 38 degrees and 52 degrees. The larger angle is:
\[ \text{Larger Angle} = 52 \text{ degrees} \]

### Final Answer:
The larger angle is **52 degrees**.