Question

look at the diagram. which equation can be used to solve for x? 4x = 70, 4x + 70 = 110, 3x + 70 = 110, 4x + 70 = 180. find the value of x. x =

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle with measure $110^{\circ}$ and the angle composed of the angles with measures $(x + 3x)^{\circ}$ and $70^{\circ}$ are vertical angles.

Step2: Set up the equation

The sum of the angles $(x + 3x)^{\circ}$ and $70^{\circ}$ is equal to the vertical - angle of measure $110^{\circ}$. Since $x+3x = 4x$, the equation is $4x + 70=110$.

Step3: Solve the equation for x

Subtract 70 from both sides of the equation $4x + 70=110$. We get $4x=110 - 70$, so $4x = 40$. Then divide both sides by 4: $x=\frac{40}{4}=10$.

Answer:

The equation to solve for x is $4x + 70 = 110$.
$x = 10$