Question

lines x and y are parallel.
write an equation that represents the relationship between c and another angle. explain how you know this equation is always true.
c + = 180 because
they are alternate interior angles
they are corresponding angles
they are vertical angles
they form a linear pair.
a + b = 180, as a linear pair. so you can substitute c for a since they are corresponding angles and therefore congruent.
a + h = 180, as a linear pair. so you can substitute c for a since they are corresponding angles and therefore congruent.

Explanation:

Step1: Identify angle - pair relationships

Given two parallel lines \(x\) and \(y\) cut by a transversal. Angle \(c\) and angle \(d\) are vertical - angles, angle \(c\) and angle \(a\) are corresponding angles. A linear pair of angles is supplementary (their sum is \(180^{\circ}\)).

Step2: Determine the relevant angle

We know that \(a + b=180^{\circ}\) because they form a linear pair. Since \(c=a\) (corresponding angles of parallel lines), we can substitute \(c\) for \(a\). So \(c + b=180^{\circ}\) because they form a linear pair.

Answer:

\(b\)