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Use the conjectures and definitions in this lesson to solve parts (a) and (b). Each part is a separate problem.

  1. If , find and by calculation.

    Angle 1 and angle 2 are alternate interior angles.

    When the lines are parallel, alternate interior angles have equal measures.

  2. If and , write an equation and find .

    Disregard your calculations for angle measure from part (a).

  3. If and , write an equation to find . Then find .

    Since the lines are parallel, angles 1 and 2 have equal measure.