Question

lines x and y are parallel. write an equation that represents the relationship between f and another angle. explain how you know this equation is always true. 1 + c = 180 because they are alternate interior angles they are corresponding angles they are vertical angles they form a linear pair. h + g = 180, as a linear pair. so you can substitute f for h since they are corresponding angles and therefore congruent h + a = 180, as a linear pair. so you can substitute f for h since they are corresponding angles and therefore congruent

Explanation:

Step1: Analyze the relationship between angles

When two parallel lines are cut by a transversal, certain angle relationships hold. A linear - pair of angles is formed when two adjacent angles form a straight line. The sum of angles in a linear pair is \(180^{\circ}\).

Step2: Identify the linear - pair relationship

We know that \(f\) and \(c\) form a linear pair. By the definition of a linear pair (two adjacent angles whose non - common sides form a straight line), the sum of the measures of the angles in a linear pair is \(180^{\circ}\). So, \(f + c=180\)

Answer:

\(f + c = 180\) because they form a Linear Pair.