Question

look at the diagram.
diagram: intersecting lines with points r, s, t, u, vertex v; angle ∠rv s = 68°, angle ∠tv u = (6x - 4)°
which equation can be used to solve for x?
options: 6x - 72 = 180, 6x - 4 = 68, 6x + 64 = 90, 2x = 68
solve for x.

Explanation:

Part 1: Determine the equation to solve for \( x \)

Step1: Identify vertical angles

Vertical angles are equal. The angle \( 68^\circ \) and the angle \( (6x - 4)^\circ \) are vertical angles.

Step2: Set up the equation

Since vertical angles are equal, we set \( 6x - 4 = 68 \).

Step1: Add 4 to both sides

To isolate the term with \( x \), add 4 to both sides of the equation \( 6x - 4 = 68 \).
\( 6x - 4 + 4 = 68 + 4 \)
\( 6x = 72 \)

Step2: Divide by 6

Divide both sides by 6 to solve for \( x \).
\( \frac{6x}{6} = \frac{72}{6} \)
\( x = 12 \)

Answer:

\( 6x - 4 = 68 \)

Part 2: Solve for \( x \)