Getting Started 
Misconception/Error The student is unable to describe the relationship between the measures of and . 
Examples of Student Work at this Level The student is unable to identify the angles as supplementary. The student makes:
 An inference that is not supported by the diagram (e.g., “ is half of ” or “” or “the angles have the same absolute value”).
 An observation that is unclear (e.g., “the angles are opposites”).
 An incorrect statement that does address the measures of the angles.
 A true statement that does not address the measures of the angles (e.g., “they are on the same side of the transversal” or “they are sameside interior angles”).
 An untrue statement that does not address the measures of the angles.

Questions Eliciting Thinking How did you determine the angle measures are equal? Can you show me how you measured them?
What do you mean by opposite? Are they vertical angles?
Do you know the names of any of the special angle pairs in the diagram?
What do you know about any of the angle pairs in the diagram? 
Instructional Implications Review the definitions of straight angle, linear pair of angles, supplementary angles, vertical angles, and transversal. Provide instruction on the angle pairs that are formed when two lines are intersected by a transversal. Provide diagrams of two lines intersected by a transversal (some of which include two parallel lines) and assist the student in identifying examples of vertical angles, linear pairs of angles, corresponding angles, alternate interior angles, and sameside interior angles. Give the student additional opportunities to identify each of these angle pairs in diagrams.
Allow the student to explore the relationships among the measures of angles formed by two lines and a transversal using tracing paper. Provide an example of two nonparallel lines intersected by a transversal and an example of two parallel lines intersected by a transversal. Ask the student to trace angles and compare each angle to the corresponding angle at the other vertex. Guide the student to observe that when the lines are parallel, corresponding angles are congruent. Encourage the student to explore the relationships among other angle pairs in the diagram. Summarize the results by stating, when two parallel lines are intersected by a transversal:
 Corresponding angles are congruent.
 Alternate interior angles are congruent.
 Sameside interior angles are supplementary.
Provide a diagram of two parallel lines intersected by a transversal with one angle measure indicated. Ask the student to identify the measures of all other angles in the diagram.

Making Progress 
Misconception/Error The student is unable to clearly justify the relationship between the measures of and . 
Examples of Student Work at this Level The student understands that and are supplementary but cannot clearly identify and justify the relationship. The student states that and :
 Make a straight line.
 Add up to 180°.

Questions Eliciting Thinking How did you determine these two angles make a straight line?
How did you determine that the measures of the angles sum to 180°? 
Instructional Implications Ask the student to explain how he or she determined that the measures of and sum to 180°. Assist the student in developing an appropriate justification based on the approach the student took. For example, if the student used tracing paper to copy the angles and redraw them so that they share a vertex and side, help the student draw a diagram that illustrates this, and devise an appropriate explanation to supplement the drawing.
Provide additional opportunities to justify the relationship between the measures of angles formed by parallel lines and a transversal. Assist the student in transitioning from using tracing paper to developing a logical argument. 
Got It 
Misconception/Error The student provides complete and correct responses to all components of the task. 
Examples of Student Work at this Level The student indicates that the measures of and sum to 180° and provides an appropriate justification. For example, the student:
 Traces both angles and then redraws them so that they share a vertex and a side, and explains that the angles form a linear pair so must be supplementary.
 Reasons logically from previously established angle relationships [e.g., (1) vertical angles are congruent and (2) when two parallel lines are intersected by a transversal, corresponding angles are congruent]. For example, the student names the angle that corresponds to as and explains that and form a linear pair and are supplementary. Since corresponds to , they are congruent. So and must also be supplementary.

Questions Eliciting Thinking Do you know the name of this kind of angle pair?
Would the measures of and still sum to 180° if lines m and n were not parallel?
Suppose the = 120°. What is the measure of each of the other angles in the diagram? 
Instructional Implications If the student used a tracing paper demonstration to explain the relationship between the measures of and , review previously established angle relationships such as: (1) vertical angles are congruent, and (2) when two parallel lines are intersected by a transversal, corresponding angles are congruent. Then ask the student to logically reason about the relationship between the measures of and .
Ask the student to provide a justification that alternate exterior angles formed by the intersection of a transversal and two parallel lines are congruent.
Consider implementing other MFAS tasks from standard 8.G.1.5 to further explore the student’s understanding of angle relationships in the context of parallel lines and a transversal. 