A number when subtracted by 1/7 of itself gives the same value as the sum of all the angles of a triangle. What is the number ?

Options

A. 224
B. 210
C. 140
D. 350

Answer

To solve the problem step by step, we can follow these instructions:

1. **Understand the Problem**: We need to find a number (let's call it \( x \)) such that when we subtract \( \frac{1}{7} \) of that number from itself, we get the same value as the sum of all angles in a triangle.

2. **Identify the Sum of Angles in a Triangle**: The sum of all angles in a triangle is \( 180^\circ \).

3. **Set Up the Equation**: According to the problem, we can express this mathematically as:
\[ x - \frac{1}{7}x = 180 \]

4. **Combine Like Terms**: To simplify the left side of the equation, we can combine the terms:
\[ x - \frac{1}{7}x = \frac{7}{7}x - \frac{1}{7}x = \frac{6}{7}x \]
So, we rewrite the equation as:
\[ \frac{6}{7}x = 180 \]

5. **Solve for \( x \)**: To isolate \( x \), we can multiply both sides of the equation by the reciprocal of \( \frac{6}{7} \), which is \( \frac{7}{6} \):
\[ x = 180 \times \frac{7}{6} \]

6. **Calculate the Value**: Now we perform the multiplication:
\[ x = 180 \times \frac{7}{6} = 30 \times 7 = 210 \]

7. **Conclusion**: Therefore, the number we are looking for is \( 210 \).