




Massachusetts Comprehensive Assessment System
2015, Grade 10 Mathematics
Question 42: OpenResponse 

Reporting Category: Geometry Standard: 10.G.3  Recognize and solve problems involving angles formed by transversals of coplanar lines. Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle. Standard: Mathematics.8.G.1.05  Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angleangle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Parallel lines q and m are cut by transversal lines j and k. The lines, and the measures of some of the angles created by the intersections of the lines, are shown in the diagram below.  What is the measure, in degrees, of ? Show or explain how you got your answer.
 What is the measure, in degrees, of ? Show or explain how you got your answer.
 What is the measure, in degrees, of ? Show or explain how you got your answer.
 What is the measure, in degrees, of ? Show or explain how you got your answer.

Scoring Guide and Sample Student Work Select a score point in the table below to view the sample student response.
Score  Description 
4 
The student response demonstrates an exemplary understanding of the Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. The student calculates angle measures in a diagram with parallel lines and transversals. 
4 
3 
The student response demonstrates a good understanding of the Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. Although there is significant evidence that the student was able to recognize and apply the concepts involved, some aspect of the response is flawed. As a result the response merits 3 points. 
2 
The student response demonstrates a fair understanding of the Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. While some aspects of the task are completed correctly, others are not. The mixed evidence provided by the student merits 2 points. 
1 
The student response demonstrates a minimal understanding of the Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal. 
0 
The student response contains insufficient evidence of an understanding of the Geometry concepts involved in using informal arguments to establish facts about the angles created when parallel lines are cut by a transversal to merit any points. 
Note: There are 2 sample student responses for Score Point 4.
Grade 10 Mathematics
 Question 17: Number and Quantity
 Question 20: Geometry
 Question 21: Algebra and Functions
 Question 36: Statistics and Probability
 Question 41: Algebra and Functions
 Question 42: Geometry
Return to the MCAS 2015 Student Work Directory
Last Updated: January 14, 2019


