An angle `x^@` is one -fourth of its supplementary angle.What is the measure of the angle `x^@` ?

Answer

To solve the problem, we need to find the measure of the angle \( x^\circ \) which is one-fourth of its supplementary angle. Let's break this down step by step.

### Step 1: Understand the concept of supplementary angles
Supplementary angles are two angles whose measures add up to \( 180^\circ \). If we have an angle \( x^\circ \), its supplementary angle can be expressed as:
\[ 180^\circ - x^\circ \]

### Step 2: Set up the equation
According to the problem, angle \( x^\circ \) is one-fourth of its supplementary angle. We can write this relationship as:
\[ x^\circ = \frac{1}{4} (180^\circ - x^\circ) \]

### Step 3: Eliminate the fraction
To eliminate the fraction, we can multiply both sides of the equation by 4:
\[ 4x^\circ = 180^\circ - x^\circ \]

### Step 4: Rearrange the equation
Next, we will rearrange the equation to isolate \( x^\circ \). We can add \( x^\circ \) to both sides:
\[ 4x^\circ + x^\circ = 180^\circ \]
This simplifies to:
\[ 5x^\circ = 180^\circ \]

### Step 5: Solve for \( x^\circ \)
Now, we can solve for \( x^\circ \) by dividing both sides by 5:
\[ x^\circ = \frac{180^\circ}{5} \]
Calculating this gives:
\[ x^\circ = 36^\circ \]

### Conclusion
The measure of the angle \( x^\circ \) is \( 36^\circ \).

---