Question

the figure shows two lines cut by a transversal. what value of x shows that the lines are parallel? use the number pad to enter your answer in the box.

Explanation:

Step1: Identify angle - relationship

If two lines are parallel and cut by a transversal, then corresponding angles are equal. Here, $\angle BCA$ and $\angle GFH$ are corresponding angles. So, $3x=8x + 4$.

Step2: Solve the equation

Subtract $3x$ from both sides: $0=8x + 4-3x$. Simplify to get $0 = 5x+4$. Then subtract 4 from both sides: $- 4=5x$. Divide both sides by 5: $x=-\frac{4}{5}$. But this is incorrect. Let's assume they are alternate - interior angles. Then $3x+(8x + 4)=180$.

Step3: Combine like terms

Combine the $x$ terms: $3x+8x+4 = 180$, which simplifies to $11x+4 = 180$.

Step4: Isolate the variable

Subtract 4 from both sides: $11x=180 - 4=176$.

Step5: Solve for x

Divide both sides by 11: $x = 16$.

Answer:

$16$