Question

look at the diagram. which equation can be used to solve for x? 7x - 34 = 90 5x = 34 2x = 34 7x + 34 = 90 solve for x. x =

Explanation:

Step1: Note vertical - angle relationship

The angles \((2x)^{\circ}\) and \((5x)^{\circ}\) together with the \(34^{\circ}\) angle and the right - angle (\(90^{\circ}\)) are related. The sum of the non - overlapping adjacent angles around a point is \(180^{\circ}\). The sum of the angles \((2x)^{\circ}\) and \((5x)^{\circ}\) and \(34^{\circ}\) and \(90^{\circ}\) is \(180^{\circ}\). But we can also consider the fact that the sum of the angles \((2x + 5x)\) and \(34^{\circ}\) is \(90^{\circ}\) (because they are complementary angles).
The sum of the angles \((2x)\) and \((5x)\) is \(7x\). So the equation based on the fact that the sum of two non - overlapping adjacent angles that form a right - angle is \(7x+34 = 90\).

Step2: Solve the equation for \(x\)

We have the equation \(7x + 34=90\).
Subtract 34 from both sides: \(7x=90 - 34\).
\(7x=56\).
Divide both sides by 7: \(x=\frac{56}{7}=8\).

Answer:

The correct equation is \(7x + 34 = 90\) and \(x = 8\)