Question

In the diagram above$\mathbf{r}\mathbf{\parallel }\mathbf{s}$.

Solve for $\mathbf{x}$:role="math" localid="1650007841155" $\mathbf{m}\mathbf{\angle }\mathbf{2}\mathbf{=}\mathbf{70}$ and$\mathbf{m}\mathbf{\angle }\mathbf{8}\mathbf{=}\mathbf{6}\mathbf{x}\mathbf{-}\mathbf{2}$.

Short answer

The value of$x$ is 12.

Step-by-step solution

Step 1. Highlight and in the given diagram.

Step 2. Apply the property of parallel lines.

If two parallel lines are intersected by a transversal then the alternate interior angles are congruent.

Step 3. Description of step.

From the given figure it can be observed that$r\parallel s$ and$t$ is transversal then by the definition of alternate interior angles,$\angle 2$ and$\angle 8$ are alternate interior angles and by property of parallel lines, $\angle 2\cong \angle 8$.

Therefore, $m\angle 2=m\angle 8$.

Step 4. Description of step.

Substitute$70$ for$m\angle 2$ and$6x-2$ for$m\angle 8$ into$m\angle 2=m\angle 8$ and simplify.

$\begin{array}{c}70=6x-2\\ 72=6x\\ x=\frac{72}{6}\\ =12\end{array}$

Therefore, the value of$x$ is 12.