An angle is `24^(@)` more than its complement. The measure of the angle is

Options

A. `47^(@)`
B. `57^(@)`
C. `53^(@)`
D. `66^(@)`

Answer

To solve the problem, we need to find the measure of an angle that is 24 degrees more than its complement. Let's break it down step by step.

### Step 1: Understand the relationship between the angle and its complement
Let the angle be represented as \( x \). The complement of an angle is what, when added to the angle, equals 90 degrees. Therefore, the complement of \( x \) can be expressed as \( 90 - x \).

### Step 2: Set up the equation
According to the problem, the angle \( x \) is 24 degrees more than its complement. This can be written as:
\[ x = (90 - x) + 24 \]

### Step 3: Simplify the equation
Now, let's simplify the equation:
\[ x = 90 - x + 24 \]
Combining like terms gives:
\[ x = 114 - x \]

### Step 4: Solve for \( x \)
Next, we will add \( x \) to both sides of the equation to isolate \( x \):
\[ x + x = 114 \]
This simplifies to:
\[ 2x = 114 \]
Now, divide both sides by 2:
\[ x = \frac{114}{2} = 57 \]

### Step 5: Conclusion
The measure of the angle is \( 57 \) degrees.

### Step 6: Find the complement
To find the complement, we can substitute \( x \) back into the complement formula:
\[ \text{Complement} = 90 - x = 90 - 57 = 33 \text{ degrees} \]

### Final Answer
The measure of the angle is \( 57 \) degrees, and its complement is \( 33 \) degrees.

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