The measure of an angle for which the measure of the supplement is four times the measure of the complement is:

Options

A. `45^@`
B. `60^@`
C. `75^@`
D. `30^@`

Answer

To solve the problem, we need to find the measure of an angle \( x \) such that its supplement is four times its complement. Let's break this down step by step.

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

### Step 2: Write the expressions for the supplement and complement
- The supplement of an angle \( x \) is given by:
\[ 180 - x \]
- The complement of an angle \( x \) is given by:
\[ 90 - x \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the supplement of the angle is four times the complement of the angle. Therefore, we can write the equation as:
\[ 180 - x = 4(90 - x) \]

### Step 4: Simplify the equation
Now, we will simplify the equation:
1. Expand the right side:
\[ 180 - x = 360 - 4x \]
2. Rearrange the equation to isolate \( x \):
\[ 180 - x + 4x = 360 \]
\[ 3x = 360 - 180 \]
\[ 3x = 180 \]

### Step 5: Solve for \( x \)
Now, divide both sides by 3:
\[ x = \frac{180}{3} = 60 \]

### Conclusion
The measure of the angle is \( 60 \) degrees.