Angle-sum link to a number: A number, when reduced by one-seventh of itself, equals the sum of the interior angles of a triangle (180 degrees). What is the number?

Introduction / Context:This is a linear equation with a familiar benchmark: the sum of angles of a triangle is 180 degrees. By expressing “one-seventh of itself” algebraically, we can solve for the number quickly.

Given Data / Assumptions:

• Let the number be N.
• N − (1/7)N = 180.
• All quantities are real numbers.

Concept / Approach:Combine like terms on the left to get a single multiple of N. Then isolate N by simple division. This is a direct single-step linear equation.

Step-by-Step Solution:

Verification / Alternative check:Compute one-seventh: N/7 = 30. Then N − N/7 = 210 − 30 = 180, which matches the triangle angle sum exactly.

Why Other Options Are Wrong:

• 224, 350: Subtracting one-seventh does not yield 180.
• 140, 189: Resulting value is not 180 when one-seventh is removed.

Common Pitfalls:Using 1/6 instead of 1/7 or confusing “one-seventh of itself” with “itself minus 7.” Read multiplicative fractions carefully.

Final Answer:210