25% of an angle is the complement of `50^(@)`. Find the angle

Options

A. `80^(@)`
B. `130^(@)`
C. `160^(@)`
D. `120^(@)`

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step 1: Understand the problem
We need to find an angle \( x \) such that 25% of this angle is equal to the complement of 50 degrees.

### Step 2: Define the angle
Let the angle be \( x \) degrees.

### Step 3: Find the complement of 50 degrees
The complement of an angle is calculated as:
\[ \text{Complement of } 50^\circ = 90^\circ - 50^\circ = 40^\circ \]

### Step 4: Set up the equation
According to the problem, 25% of the angle \( x \) is equal to the complement of 50 degrees:
\[ 25\% \text{ of } x = 40^\circ \]
This can be expressed mathematically as:
\[ \frac{25}{100} \times x = 40^\circ \]

### Step 5: Simplify the equation
We can simplify \( \frac{25}{100} \) to \( \frac{1}{4} \):
\[ \frac{1}{4} \times x = 40^\circ \]

### Step 6: Solve for \( x \)
To find \( x \), we can multiply both sides of the equation by 4:
\[ x = 40^\circ \times 4 \]
Calculating this gives:
\[ x = 160^\circ \]

### Conclusion
The angle \( x \) is \( 160^\circ \).

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