Find the angle which is double of its supplement

Options

A. `40^(@)`
B. `120^(@)`
C. `160^(@)`
D. `180^(@)`

Answer

To find the angle which is double of its supplement, we can follow these steps:

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

### Step 2: Define the supplement of the angle
The supplement of the angle \( x \) is given by:
\[ 180^\circ - x \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the angle \( x \) is double its supplement. Therefore, we can write the equation:
\[ x = 2 \times (180^\circ - x) \]

### Step 4: Expand the equation
Expanding the right side of the equation gives:
\[ x = 360^\circ - 2x \]

### Step 5: Rearrange the equation
Now, we can rearrange the equation to isolate \( x \):
\[ x + 2x = 360^\circ \]
\[ 3x = 360^\circ \]

### Step 6: Solve for \( x \)
Now, divide both sides by 3:
\[ x = \frac{360^\circ}{3} = 120^\circ \]

### Conclusion
The angle which is double of its supplement is:
\[ \boxed{120^\circ} \]