An angle is double its complement. Find the angle

Options

A. `150^(@)`
B. `60^(@)`
C. `30^(@)`
D. `120^(@)`

Answer

To solve the problem where an angle is double its complement, we can follow these steps:

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

### Step 2: Write the expression for the complement
The complement of the angle \( x \) is given by:
\[ 90 - x \text{ degrees} \]

### Step 3: Set up the equation based on the problem statement
According to the problem, the angle \( x \) is double its complement. Therefore, we can write the equation:
\[ x = 2(90 - x) \]

### Step 4: Expand the equation
Now, we will expand the right side of the equation:
\[ x = 180 - 2x \]

### Step 5: Rearrange the equation
To isolate \( x \), we will add \( 2x \) to both sides:
\[ x + 2x = 180 \]
This simplifies to:
\[ 3x = 180 \]

### Step 6: Solve for \( x \)
Now, divide both sides by 3:
\[ x = \frac{180}{3} = 60 \]

### Step 7: Conclusion
Thus, the angle is:
\[ \boxed{60 \text{ degrees}} \]

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