The angle whose supplement is three times its complement is `"____________________"`.

Options

A. `45^(@)`
B. `50^@`
C. `25^@`
D. `65^@`

Answer

To find the angle whose supplement is three times its complement, we can follow these steps:

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

### Step 2: Write the expressions for the supplement and complement
- The supplement of the angle \( x \) is given by:
\[ \text{Supplement} = 180^\circ - x \]
- The complement of the angle \( x \) is given by:
\[ \text{Complement} = 90^\circ - x \]

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

### Step 4: Simplify the equation
Now, let's simplify the equation:
\[ 180^\circ - x = 270^\circ - 3x \]

### Step 5: Rearrange the equation
To isolate \( x \), we can rearrange the equation:
\[ 180^\circ - x + 3x = 270^\circ \]
This simplifies to:
\[ 180^\circ + 2x = 270^\circ \]

### Step 6: Solve for \( x \)
Now, subtract \( 180^\circ \) from both sides:
\[ 2x = 270^\circ - 180^\circ \]
\[ 2x = 90^\circ \]
Now, divide both sides by 2:
\[ x = \frac{90^\circ}{2} = 45^\circ \]

### Conclusion
The angle whose supplement is three times its complement is:
\[ \boxed{45^\circ} \]