An angle is `30^@` more than one half of its complement. Find the angle in degrees.

Options

A. `60^@`
B. `50^@`
C. `45^@`
D. `80^@`

Answer

To solve the problem, we need to find the angle \( x \) that is 30 degrees more than half of its complement. Let's break down the steps:

### Step 1: Define the variables
Let \( x \) be the angle we want to find. The complement of \( x \) is given by \( 90 - x \) since the sum of complementary angles is 90 degrees.

### Step 2: Set up the equation
According to the problem, the angle \( x \) is 30 degrees more than half of its complement. We can express this relationship mathematically:
\[ x = \frac{1}{2}(90 - x) + 30 \]

### Step 3: Simplify the equation
Now, we will simplify the equation:
\[ x = \frac{90 - x}{2} + 30 \]
Multiply both sides by 2 to eliminate the fraction:
\[ 2x = 90 - x + 60 \]
Combine like terms:
\[ 2x + x = 150 \]
This simplifies to:
\[ 3x = 150 \]

### Step 4: Solve for \( x \)
Now, divide both sides by 3:
\[ x = \frac{150}{3} = 50 \]

### Step 5: Conclusion
The angle \( x \) is \( 50 \) degrees.

### Final Answer
The angle is \( 50 \) degrees.

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