If two complementary angles differ by `14^@` , find the angles.

Answer

To solve the problem of finding two complementary angles that differ by \(14^\circ\), we can follow these steps:

### Step 1: Define the angles
Let one angle be \(x\). Since the angles are complementary, the other angle will be \(90^\circ - x\).

### Step 2: Set up the equation
According to the problem, the difference between the two angles is \(14^\circ\). Therefore, we can write the equation:
\[ x - (90^\circ - x) = 14^\circ \]

### Step 3: Simplify the equation
Now, simplify the equation:
\[ x - 90^\circ + x = 14^\circ \]
\[ 2x - 90^\circ = 14^\circ \]

### Step 4: Solve for \(x\)
Add \(90^\circ\) to both sides:
\[ 2x = 14^\circ + 90^\circ \]
\[ 2x = 104^\circ \]
Now, divide by \(2\):
\[ x = \frac{104^\circ}{2} = 52^\circ \]

### Step 5: Find the second angle
Now, substitute \(x\) back to find the second angle:
\[ 90^\circ - x = 90^\circ - 52^\circ = 38^\circ \]

### Conclusion
The two complementary angles are \(52^\circ\) and \(38^\circ\).

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