Because 18n = 45k → 2n = 5k → n = 5a, k = 2a → θ = 18×5a = 90a → so only multiples of 90.

Tue, 05 May 2026 01:05:36 +0000

Why 18n = 45k Implies Only Multiples of 90: A Simple Mathematical Breakdown When solving equations involving variables, especially in algebra, understanding the chain of logic can clarify their implications. One such equation—18ₙ = 45ₖ—may seem straightforward, but unpacking it reveals deeper relationships that define specific values. Let’s explore step-by-step why this equation leads uniquely to θ = 90a, meaning only multiples of 90 are valid solutions. ### The Equation: 18ₙ = 45ₖ This notation expresses a proportional relationship between two expressions: 18 times the unknown variable n, and 45 times another unknown variable k. At first glance, the equation seems symbolic, but we can simplify it through algebraic manipulation.