Find the an angle which is `5^(@)` more than four times its supplement

Options

A. `145^(@)`
B. `140^(@)`
C. `35^(@)`
D. `40^(@)`

Answer

To solve the problem of finding an angle that is 5 degrees more than four times its supplement, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Angle**:
Let the angle be \( x \) degrees.

2. **Find the Supplement**:
The supplement of the angle \( x \) is given by:
\[ 180 - x \text{ degrees} \]

3. **Set Up the Equation**:
According to the problem, the angle \( x \) is 5 degrees more than four times its supplement. We can express this as:
\[ x = 4(180 - x) + 5 \]

4. **Expand the Equation**:
Now, we will expand the right side of the equation:
\[ x = 720 - 4x + 5 \]
Simplifying this gives:
\[ x = 725 - 4x \]

5. **Combine Like Terms**:
To isolate \( x \), add \( 4x \) to both sides of the equation:
\[ x + 4x = 725 \]
This simplifies to:
\[ 5x = 725 \]

6. **Solve for \( x \)**:
Now, divide both sides by 5:
\[ x = \frac{725}{5} \]
Performing the division gives:
\[ x = 145 \]

7. **Conclusion**:
Therefore, the angle is \( 145 \) degrees.

### Final Answer:
The angle is \( 145 \) degrees.

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