The angles which is four times more than its complement is

Options

A. `120^@`
B. `144^@`
C. `150^@`
D. `100^@`

Answer

To solve the problem, we need to find an angle that is four times more than its complement. Let's break this down step by step.

### Step-by-Step Solution:

1. **Understanding Complementary Angles**:
- Two angles are complementary if their sum is 90 degrees. For an angle \( x \), its complement can be calculated as \( 90 - x \).

2. **Setting Up the Equation**:
- If the angle is \( x \), then according to the problem, we can express the relationship as:
\[ x = 4 \times (90 - x) \]

3. **Expanding the Equation**:
- Distributing the 4 on the right side:
\[ x = 360 - 4x \]

4. **Rearranging the Equation**:
- Adding \( 4x \) to both sides to combine like terms:
\[ x + 4x = 360 \]
\[ 5x = 360 \]

5. **Solving for \( x \)**:
- Dividing both sides by 5:
\[ x = \frac{360}{5} = 72 \]

6. **Finding the Complement**:
- Now, we can find the complement of \( 72 \):
\[ 90 - 72 = 18 \]

7. **Checking the Condition**:
- We need to check if \( 72 \) is indeed four times its complement:
\[ 4 \times 18 = 72 \]
- This confirms that \( 72 \) is four times its complement.

### Final Answer:
The angle which is four times more than its complement is \( 72 \) degrees.