Two complementary angles differ by `12^@` Find them .

Answer

To solve the problem of finding two complementary angles that differ by 12 degrees, we can follow these steps:

### Step 1: Understand the concept of complementary angles
Complementary angles are two angles whose sum is 90 degrees.

### Step 2: Define the angles
Let one angle be \( x \) degrees. Since the angles are complementary, the other angle can be expressed as \( 90 - x \) degrees.

### Step 3: Set up the equation based on the given information
According to the problem, the two angles differ by 12 degrees. This can be expressed mathematically as:
\[ (90 - x) - x = 12 \]

### Step 4: Simplify the equation
Now, simplify the equation:
\[ 90 - x - x = 12 \]
Combine like terms:
\[ 90 - 2x = 12 \]

### Step 5: Solve for \( x \)
To isolate \( x \), first subtract 90 from both sides:
\[ -2x = 12 - 90 \]
\[ -2x = -78 \]
Now, divide both sides by -2:
\[ x = \frac{-78}{-2} = 39 \]

### Step 6: Find the second angle
Now that we have \( x \), which is 39 degrees, we can find the second angle:
\[ 90 - x = 90 - 39 = 51 \]

### Conclusion
The two complementary angles are:
- First angle: \( 39^\circ \)
- Second angle: \( 51^\circ \)

### Summary of the solution:
The two complementary angles that differ by 12 degrees are 39 degrees and 51 degrees.

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