The complement of and angles is `(1)/(4)th` of the a right . Find the angle.

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the Problem
We need to find an angle \( x \) such that its complement is one-fourth of a right angle.

### Step 2: Define the Complement
The complement of an angle \( x \) is given by:
\[ 90^\circ - x \]

### Step 3: Set Up the Equation
According to the problem, the complement of angle \( x \) is one-fourth of a right angle (which is \( 90^\circ \)):
\[ 90^\circ - x = \frac{1}{4} \times 90^\circ \]

### Step 4: Calculate One-Fourth of a Right Angle
Calculating one-fourth of \( 90^\circ \):
\[ \frac{1}{4} \times 90^\circ = 22.5^\circ \]
Now we can rewrite our equation:
\[ 90^\circ - x = 22.5^\circ \]

### Step 5: Solve for \( x \)
To find \( x \), we can rearrange the equation:
\[ x = 90^\circ - 22.5^\circ \]
Calculating this gives:
\[ x = 67.5^\circ \]

### Step 6: Conclusion
The angle \( x \) is:
\[ \boxed{67.5^\circ} \]

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