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Find the measures of the angles requested and explain how you found them.  Each part is a separate problem. 

  1. If , find  .

    Angle 4 is supplementary with angle 2, which corresponds to angle 6. Since the lines cut by the transversal are parallel, corresponding angles are equal.

  2. If  , find  

    Angle 1 and angle 4 are vertical angles, which are always equal. In addition, angle 4 and angle 8 are corresponding angles.

  3. If  , find  .

    Angle 2 and angle 6 are corresponding angles. Since the lines are parallel, they will have equal measure. Angle 6 and angle 8 are supplementary. 

2 horizontal parallel lines are crossed by a transversal line, with angles labeled as follows: Upper intersection: exterior left, 1, exterior right, 2, interior right, 4, and, interior left, 3. Lower intersection: interior left, 5, interior right, 6, exterior right 8, and exterior left, 7.