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

Answer

To solve the problem step by step, let's break it down clearly:

### Step 1: Understand the complement of an angle
The complement of an angle \( x \) is given by the formula:
\[ \text{Complement} = 90^\circ - x \]

### Step 2: Set up the equation
According to the problem, the complement of the angle \( x \) is equal to one fourth of a right angle (which is \( 90^\circ \)). Therefore, we can write the equation as:
\[ 90^\circ - x = \frac{1}{4} \times 90^\circ \]

### Step 3: Calculate one fourth of a right angle
Calculating one fourth of \( 90^\circ \):
\[ \frac{1}{4} \times 90^\circ = 22.5^\circ \]
Now, substitute this value back into the equation:
\[ 90^\circ - x = 22.5^\circ \]

### Step 4: Solve for \( x \)
To find \( x \), rearrange the equation:
\[ x = 90^\circ - 22.5^\circ \]
Calculating the right side:
\[ x = 67.5^\circ \]

### Step 5: Conclusion
Thus, the angle \( x \) is:
\[ \boxed{67.5^\circ} \]

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