Question

Complete each statement with the word always, sometimes, or never.

If two lines are cut by a transversal and same-side interior angles are complementary, then the lines are $\underset{¯}{?}$ parallel.

Short answer

If two lines are cut by a transversal and same-side interior angles are complementary, then the lines are never parallel.

Step-by-step solution

Step 1. Definition of complementary angles and supplementary angles.

The complementary angles are the angles whose sum is $\mathbf{90}\mathbf{°}$.

The supplementary angles are the angles whose sum is $\mathbf{180}\mathbf{°}$.

Step 2. Description of step.

If two lines are parallel and cut by a transversal then the same-side interior angles are supplementary.

Step 3. Write the conclusion.

Therefore, if the two lines are parallel and cut by a transversal then the same-side interiorangles are supplementary.

Therefore, if two lines are cut by a transversal and same-side interior angles are complementary, then the lines are never parallel.