When two parallel lines are “cut” by a transversal, some special properties arise. We will begin by stating these properties, and then we can use these properties to solve some problems.

**PROPERTY 1:** When two parallel lines are cut by a transversal, then corresponding angles are congruent.

In the diagram below, angles 1 and 5 are corresponding, and so they are equal. Similarly with angles 4 and 8, etc.

**PROPERTY 2:** When two parallel lines are cut by a transversal, then adjacent angles are supplementary. That is, when two parallel lines are cut by a transversal, then the sum of adjacent angles is \(180^\circ \).

In the diagram above, this property tells us that angles 1 and 2 sum to \(180^\circ \). Similarly with angles 5 and 6.

**EXAMPLE:** Solve for \(x\).

**SOLUTION:** From property 2, we know that the 2 angles \(x + 75\), and \(A\) (so called by me) are supplementary. That is,

\(x + 75 + A = 180\)

But from property 1, we know that \(A = x + 125\), since those two angles are corresponding. Then \(x + 75 + x + 125 = 180\), so that \(2x + 200 = 180\). Then \(2x = - 20\), and \(x = - 10\).

**EXAMPLE:** Solve for \(x\).

**SOLUTION:** Since, by property 1, we know that corresponding angles are congruent, we know that

\(12x + 3 = 11x + 9\)

\(x = 6\)

Below you can **download** some **free** math worksheets and practice.

Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Solve for x.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**

Find the measure of the angle indicated in bold.

This free worksheet contains 10 assignments each with 24 questions with answers.**Example of one question:**

**Watch below how to solve this example:**