Question

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

Solve for $\mathbf{y}$:$\mathit{m}\mathbf{\angle }\mathbf{3}\mathbf{=}\mathbf{8}\mathit{y}\mathbf{-}\mathbf{40}$ and$\mathit{m}\mathbf{\angle }\mathbf{8}\mathbf{=}\mathbf{2}\mathit{y}\mathbf{+}\mathbf{20}$.

Short answer

The value of$y$ is 20.

Step-by-step solution

Step 1. Highlight ∠3 and ∠8 in the given diagram.

Step 2. Apply the property of parallel lines.

If two parallel lines are intersected by a transversal then the same side interior angles are supplementary.

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 same side interior angles,$\angle 3$ and$\angle 8$ are same side interior angles and by property of parallel lines, $m\angle 3+m\angle 8=180$.

Step 4. Description of step.

Substitute $8y-40$for $m\angle 3$and $2y+20$for$m\angle 8$ into$m\angle 3+m\angle 8=180$ and simplify to obtain the value of y.

$\begin{array}{r}8y-40+2y+20=180\\ 10y-20=180\\ 10y=200\\ y=20\end{array}$

Therefore, the value of$y$ is 20.