Question

elaina is making a quilt following the pattern shown below. if all the horizontal lines are parallel, what is the value of x?
show or explain how you solved.
include the equation you used, the reasoning for the equation, and your solution for x.

Explanation:

Step1: Use the property of same - side interior angles

When two parallel lines are cut by a transversal, same - side interior angles are supplementary. That is, \(x+(3x + 20)=180\).

Step2: Solve the equation

Combine like terms: \(x+3x+20 = 180\), which simplifies to \(4x+20=180\).
Subtract 20 from both sides: \(4x=180 - 20\), so \(4x=160\).
Divide both sides by 4: \(x=\frac{160}{4}\).

Answer:

\(x = 40\)