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

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Solve this multiple-choice question and choose the correct option.

Accepted Answer

Introduction / Context:This algebra problem connects fractions of a number with a known constant from geometry: the sum of angles of a triangle is 180 degrees. It checks the ability to translate words into an equation and solve for the unknown efficiently. Given Data / Assumptions: Let the unknown number be x. One-seventh of x is x / 7. Sum of angles of any triangle = 180. Concept / Approach:Translate the sentence directly: x - (x / 7) = 180. Combine like terms and solve for x using simple fraction arithmetic. Step-by-Step Solution: Start with x - x/7 = 180.Compute the coefficient: 1 - 1/7 = 6/7, so (6/7) * x = 180.Isolate x: x = 180 * (7/6).Simplify: 180/6 = 30, so x = 30 * 7 = 210. Verification / Alternative check:Check: 1/7 of 210 is 30; 210 - 30 = 180, which matches the triangle angle sum. Why Other Options Are Wrong:224, 140, 350, and 126 do not satisfy x - x/7 = 180 when substituted. Common Pitfalls:Subtracting 1/7 incorrectly (e.g., using 1/6 by mistake) or mixing degrees and radians—but only the value 180 matters here. Final Answer:210

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

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