How many degrees are there in an angle which equals one - fifth of its supplement?

Options

A. `15^(@)`
B. `30^(@)`
C. `75^(@)`
D. `150^(@)`

Answer

To solve the problem of finding how many degrees are in an angle that equals one-fifth of its supplement, we can follow these steps:

### Step 1: Define the angle
Let the angle be represented by \( x \) degrees.

### Step 2: Determine the supplement of the angle
The supplement of an angle is calculated as:
\[ \text{Supplement} = 180^\circ - x \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the angle \( x \) is equal to one-fifth of its supplement. Therefore, we can write the equation:
\[ x = \frac{1}{5} \times (180^\circ - x) \]

### Step 4: Clear the fraction by multiplying both sides by 5
To eliminate the fraction, multiply both sides of the equation by 5:
\[ 5x = 180^\circ - x \]

### Step 5: Rearrange the equation
Now, add \( x \) to both sides to get all terms involving \( x \) on one side:
\[ 5x + x = 180^\circ \]
This simplifies to:
\[ 6x = 180^\circ \]

### Step 6: Solve for \( x \)
Now, divide both sides by 6 to find the value of \( x \):
\[ x = \frac{180^\circ}{6} = 30^\circ \]

### Conclusion
Thus, the angle that equals one-fifth of its supplement is:
\[ \boxed{30^\circ} \]

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