An angle is one-fifth of its supplement. The measure of the angle is

Options

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

Answer

To solve the problem where an angle is one-fifth of its supplement, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angle**:
Let the angle be \( x \).

2. **Define the Supplementary Angle**:
The supplementary angle is given by \( 180^\circ - x \).

3. **Set Up the Equation**:
According to the problem, the angle \( x \) is one-fifth of its supplement. Therefore, we can write the equation:
\[ x = \frac{1}{5}(180^\circ - x) \]

4. **Multiply Both Sides by 5**:
To eliminate the fraction, multiply both sides by 5:
\[ 5x = 180^\circ - x \]

5. **Rearrange the Equation**:
Add \( x \) to both sides to get all terms involving \( x \) on one side:
\[ 5x + x = 180^\circ \]
This simplifies to:
\[ 6x = 180^\circ \]

6. **Solve for \( x \)**:
Divide both sides by 6 to find the value of \( x \):
\[ x = \frac{180^\circ}{6} = 30^\circ \]

7. **Find the Supplementary Angle**:
Now, we can find the supplementary angle:
\[ 180^\circ - x = 180^\circ - 30^\circ = 150^\circ \]

### Final Answer:
The measure of the angle is \( 30^\circ \).

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