Ohio Grade 8 Achievement Test for Mathematics – May 2008
Annotated Item 5
Standard and Benchmark Assessed:
Standard:
Geometry and Spatial Sense
Benchmark:
C. Recognize and apply angke relationship in situations involving intersecting
lines, perpendicular lines and parallel lines
Multiple Choice Question:
5.
A parallelogram is shown.
What is the measure of angle F?
A.
B.
C.
D.
45 degrees
65 degrees
90 degrees
135 degrees
Commentary:
This multiple-choice question asks students to find the measure of an angle in a parallelogram.
To solve the problem students may use geometric concepts related to parallel lines cut by a
transversal or the properties of parallelograms. One method for finding the measure of angle F
is to use geometric concepts related to parallel lines cut by a transversal.
↔
↔
Angles E and F are located between two parallel lines (EH and FG) and on the same side of
↔
transversal (EF), and the sum of their measures is 180 degrees:
m  E + m  F = 180°
135 + m  F = 180°
m  F = 45°
Another method for finding the measure of angle F is to use properties of parallelograms. In
parallelograms, the opposite angles are congruent (measures of angles E and G are equal, as
well as measures of angles F and H) and the sum of all angle measures in a parallelogram is
360°. If the measure of angle F is x and the measure of angle H is also x, then the following
equation can be solved to find the missing measure of angle F:
135 + 135 + x + x = 360
270 + 2x = 360
Source: Ohio Department of Education
July 08
Ohio Grade 8 Achievement Test for Mathematics – May 2008
Annotated Item 5
2x = 90
x = 45
m  F = 45°
The measure of angle F is 45 degrees, answer choice A.
Answer choices B and C are incorrect because the student made a computational error. Answer
choice D is incorrect because students thought that all angles of a parallelogram must be equal
and the measure of angle F is also 135 degrees.
The complexity level of this question is Moderate Complexity. This question requires students to
retrieve information from a figure and represent a situation mathematically.
Performance Data:
The percent of public school students selecting answer choice A for question 5 on the May 2008
Grade 8 Achievement Test was 74%.
Keywords: geometry, angle, measure of an angle, parallelogram, parallel lines
Source: Ohio Department of Education
July 08