Question

look at the diagram. which equation can be used to solve for x? 8x + 42 = 180 8x + 164 = 180 8x + 42 = 122 8x - 42 = 122 solve for x. x =

Explanation:

Step1: Analyze angle - relationship

We know that vertical angles are equal. The angle of \(122^{\circ}\) and the non - labeled angle composed of \((8x)^{\circ}\) and \(42^{\circ}\) are vertical angles, so \(8x + 42=122\).

Step2: Solve the equation for \(x\)

Subtract 42 from both sides of the equation \(8x + 42 = 122\), we get \(8x=122 - 42\), that is \(8x = 80\). Then divide both sides by 8, \(x=\frac{80}{8}=10\).

Answer:

The equation is \(8x + 42 = 122\), \(x = 10\)