Question

lines x and y are parallel. write an equation that represents the relationship between b and c. type your answer in the box. explain how you know this equation is always true.

Explanation:

Step1: Use the property of parallel lines and transversal

When two parallel lines \(x\) and \(y\) are cut by a transversal, \(b\) and \(c\) are same - side interior angles.

Step2: Recall the theorem for same - side interior angles

The theorem states that same - side interior angles are supplementary. So, \(b + c=180\)

of why the equation is always true:
Lines \(x\) and \(y\) are parallel. When a transversal intersects two parallel lines, the sum of same - side interior angles (\(b\) and \(c\) in this case) is \(180^{\circ}\) by the Same - Side Interior Angles Theorem.

Answer:

\(b + c = 180\)