Find the measure of an angle if seven times its complement is `10^(@)` less than three times its supplement .

Options

A. `25^(@)`
B. `50^(@)`
C. `100^(@)`
D. None of these

Explanation

To find the measure of an angle \( x \) such that seven times its complement is 10 degrees less than three times its supplement, we can follow these steps:

### Step-by-step Solution

1. **Define the angle**: Let the measure of the required angle be \( x \) degrees.

2. **Find the complement and supplement**:
- The complement of the angle \( x \) is \( 90 - x \) degrees.
- The supplement of the angle \( x \) is \( 180 - x \) degrees.

3. **Set up the equation**: According to the problem, seven times the complement is 10 degrees less than three times the supplement. This can be written as:
\[ 7(90 - x) = 3(180 - x) - 10 \]

4. **Expand both sides**:
- Left side: \( 7(90 - x) = 630 - 7x \)
- Right side: \( 3(180 - x) - 10 = 540 - 3x - 10 = 530 - 3x \)

Thus, the equation becomes:
\[ 630 - 7x = 530 - 3x \]

5. **Rearrange the equation**: Move all terms involving \( x \) to one side and constant terms to the other side:
\[ 630 - 530 = 7x - 3x \]
Simplifying this gives:
\[ 100 = 4x \]

6. **Solve for \( x \)**: Divide both sides by 4:
\[ x = \frac{100}{4} = 25 \]

7. **Conclusion**: The measure of the angle is \( 25 \) degrees.