Question

the figure shows two lines cut by a transversal. which value of x shows that the lines are parallel? if two lines cut by a transversal are parallel, then same - side exterior angles must be supplementary.

Explanation:

Step1: Set up the equation

Since same - side exterior angles are supplementary when lines are parallel, we have $(4x - 10)+(x + 20)=180$.

Step2: Combine like terms

Combining the $x$ terms and the constant terms, we get $4x+x-10 + 20=180$, which simplifies to $5x+10 = 180$.

Step3: Isolate the variable term

Subtract 10 from both sides: $5x+10-10=180 - 10$, resulting in $5x=170$.

Step4: Solve for $x$

Divide both sides by 5: $\frac{5x}{5}=\frac{170}{5}$, so $x = 34$.

Answer:

34