Question

lines r and s are parallel and cut by transversal t. what is the value of x?

Explanation:

Step1: Identify angle - relationship

The angles $(6x + 4)^{\circ}$ and $(2x)^{\circ}$ are alternate - interior angles. Since lines $r$ and $s$ are parallel and cut by a transversal $t$, alternate - interior angles are congruent. So, $6x+4 = 2x$.

Step2: Solve the equation for $x$

Subtract $2x$ from both sides: $6x - 2x+4=2x - 2x$, which simplifies to $4x+4 = 0$. Then subtract 4 from both sides: $4x+4 - 4=0 - 4$, getting $4x=-4$. Divide both sides by 4: $\frac{4x}{4}=\frac{-4}{4}$, so $x=-1$.

Answer:

$x = - 1$