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

Options

A. `30^(@)`
B. `35^(@)`
C. `25^(@)`
D. `20^(@)`

Answer

To solve the problem, we need to find the measure of an angle \( x \) such that seven times its complement is 10 degrees less than three times its supplement.

### Step-by-Step Solution:

1. **Define the Angle and Its Complement and Supplement:**
- Let the angle be \( x \).
- The complement of the angle is \( 90^\circ - x \).
- The supplement of the angle is \( 180^\circ - x \).

2. **Set Up the Equation Based on the Problem Statement:**
- According to the problem, seven times the complement is 10 degrees less than three times the supplement.
- This can be expressed mathematically as:
\[ 7(90^\circ - x) = 3(180^\circ - x) - 10 \]

3. **Expand Both Sides of the Equation:**
- Expanding the left side:
\[ 7(90^\circ - x) = 630^\circ - 7x \]
- Expanding the right side:
\[ 3(180^\circ - x) - 10 = 540^\circ - 3x - 10 = 530^\circ - 3x \]

4. **Set the Expanded Equations Equal to Each Other:**
- Now we have:
\[ 630^\circ - 7x = 530^\circ - 3x \]

5. **Rearrange the Equation to Solve for \( x \):**
- Bring all terms involving \( x \) to one side and constant terms to the other side:
\[ 630^\circ - 530^\circ = 7x - 3x \]
\[ 100^\circ = 4x \]

6. **Divide Both Sides by 4 to Find \( x \):**
- Now, divide both sides by 4:
\[ x = \frac{100^\circ}{4} = 25^\circ \]

7. **Conclusion:**
- The measure of the angle is \( 25^\circ \).