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Home > CCG > Chapter 6 > Lesson 6.1.4 > Problem 6-34

6-34.

Use your theorems about parallel lines and the angles formed with a third line to find the measures of the labeled angles below. Show each step you use and be sure to justify each one with an angle theorem from your Angle Relationships Toolkit. Be sure to write down your reasoning in the order that you find the angles.

  1. A transversal line cuts two horizontal parallel lines. About the point of intersection, of the top parallel line and the transversal, are exterior right angle, a, and interior left angle, b. About the point of intersection, of the bottom parallel line and the transversal, are interior left angle, c, and interior right angle, 123 degrees.

    There are multiple correct ways to find the angle measures.

    If parallel lines are cut by a transversal, then
    corresponding angles have equal measures.

    Vertical angles must also have equal measures.

    The angle corresponds to which angle?

    because corresponding angles on parallel lines have equal measures.

    because vertical angles have equal measures.

    because they are supplementary angles.

    So what is ?

    , ,

  1. A transversal line cuts two horizontal parallel lines. About the point of intersection, of the top parallel line and the transversal, are exterior left angle, d, and interior right angle, e. About the point of intersection, of the bottom parallel line and the transversal, are interior left angle, f, and exterior left angle, 82 degrees.

    , ,

    Make sure you write down your reasoning.

  1. A transversal line cuts two horizontal parallel lines. About the point of intersection, of the top parallel line and the transversal, is interior left angle, 75 degrees. About the point of intersection, of the bottom parallel line and the transversal, are interior left angle, g, and exterior right angle, h.