Alternate Interior and Exterior Angles —Practice Geometry Questions

By Allen Ma, Amber Kuang

When two parallel lines are intersected by a third line (called a transversal), congruent pairs of angles are formed, including alternate interior angles and alternate exterior angles.

The following practice questions ask you to use this information to find a missing angle, and then to apply some algebra to calculate a missing variable.

Practice questions

Use the diagram and the given information to solve the problem.

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  1. Parallel lines

    image1.png

    are cut by a transversal. If

    image2.png

    is represented by

    image3.png

    is represented by 4x – 45, find the value of x.

  2. Parallel lines

    image4.png

    are cut by a transversal. If

    image5.png

    are represented by

    image6.png

    respectively, find the degree measure of

    image7.png

Answers and explanations

  1. 20

    image8.png

    are alternate interior angles. Alternate interior angles are congruent, so set their measures equal to each other and solve for x:

    image9.png

  2. 140 degrees

    image10.png

    are alternate exterior angles. Alternate exterior angles are congruent, so set their measures equal to each other and solve for x:

    image11.png

    which means they add up to 180 degrees. Use this info to solve for

    image12.png