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Home > CCG > Chapter 5 > Lesson 5.3.5 > Problem 5-133


Examine trapezoid  below.  

Trapezoid A, B, C, D. Point E is made on side A, D. Point E is the vertex for a triangle B, E, C within the trapezoid. Angle A is 40 degrees and angle D is 60 degrees. Side A, B is parallel to side C, E. Side B,E is parallel to side C D. Side A, E is parallel to side B, C.

  1. Find the measures of all the angles in the diagram.

    The corresponding angles are equal.

    Since line line , then corresponding angles .
    So , mark it on your diagram.
    While line line , then corresponding angles .
    So , mark it on your diagram.

    Use the Triangle Angle Sum Theorem.

    Now you know two angles in and , knowing that one angle is and .
    Calculate the third angle using the equation .
    So the missing angle is . Mark it in your diagram.

    The angles at E form a straight angle, which is .

    Since and then .
    Solve for , mark it on your diagram. .

    The alternate interior angles are equal.

    Since and , then and  because alternate angles are equal. Mark the angles on your diagram.

    Angle B, E, A is 60 degrees. Angle C, E, D, is 40 degrees.

    Angle B is A, B, E, is 80 degrees and angle D, C, E, is 80 degrees.

    Angle B, E, C, is 80 degrees.

    Angle E, B, C, is 60 degrees. Angle B, C, E, is 40 degrees.

  2. What is the sum of the angles that make up the trapezoid ? That is, what is ?

    Note: Do not add in the angles at .