When one-seventh of a number is subtracted from the number itself, the result equals the sum of the angles in a triangle (180 degrees). What is the number?

Introduction / Context:
This is a linear equation in one variable with a familiar constant (the angle sum of a triangle). Converting the verbal statement into an algebraic equation and solving it yields the unique value of the number.

Given Data / Assumptions:

• Let the number be N.
• The sum of angles in a triangle is 180 degrees.
• Condition: N − (1/7)N = 180.

Concept / Approach:
Combine like terms on the left: N − (1/7)N = (6/7)N. Then isolate N by dividing 180 by the fractional coefficient. This is a direct application of fraction arithmetic.

Step-by-Step Solution:

Verification / Alternative check:
Check: 210 − (1/7)*210 = 210 − 30 = 180, which satisfies the given relation.

Why Other Options Are Wrong:
224, 140, 350, and 196 do not produce 180 after subtracting one-seventh of themselves.

Common Pitfalls:
Subtracting 1/7 incorrectly (e.g., taking N − 1/7 instead of N − N/7), or miscomputing 180 * 7/6.

Final Answer:
210