Question

look at the diagram. which equation can be used to solve for x? 11x - 6 = 71, 2x + 3 = 71, 7x - 6 = 71, 2x + 3x = 71. solve for x. x =

Explanation:

Step1: Set up the equation

From the angle - relationship in the diagram, we assume that the sum of the two non - overlapping angles equals the larger angle. So, \(2x+3x = 71\) is incorrect as it doesn't match the given angle expressions. The correct equation based on the angle expressions \(2x\) and \(9x - 6\) and the known angle of \(71^{\circ}\) is \(2x+(9x - 6)=71\).

Step2: Simplify the left - hand side

Combine like terms: \(2x+9x-6=71\), which simplifies to \(11x - 6=71\).

Step3: Solve for \(x\)

Add 6 to both sides of the equation: \(11x-6 + 6=71 + 6\), so \(11x=77\).
Then divide both sides by 11: \(x=\frac{77}{11}=7\).

Answer:

\(x = 7\)