2 x− 30 ◦=x+ 60 ◦ Both angles have a measure of 150 degrees.
x= 90 ◦- The outer rays of two adjacent angle with measures 4x+ 10 ◦and 5x− 10 ◦are perpendicular. Find the measures
of each angle.
Answer:
5 x− 10 + 4 x+ 10 = 90 The angles have measures of 50 degrees and 40 degrees.
x= 10- The angles of a linear pair have measures 3x+ 45 ◦and 2x+ 35 ◦. Find the measure of each angle.
Answer:
2 x+ 35 + 3 x+ 45 = 180 The angles have measures of 105 degrees and 75 degrees.
x= 20Encourage students to take the time to write out and solve the equation neatly. This process helps them avoid
errors. Many times students will find the value ofx, and then stop without plugging in the value to the expression
for the angle measures. Have the students verify that their final answers are angle measures that have the desired
relationship.
Additional Exercise:
- Perpendicular lines form an angle with measure 8x+ 10 ◦. What is the value ofx?
Answer:
8 x+ 10 ◦= 90 ◦
x= 10 ◦Perpendicular Transversals
The Perpendicular Distance –In theory, measuring along a perpendicular line makes sense to the students, but in
practice, when lining up the ruler or deciding which points to put in the distance formula, there are many distractions.
Students can evaluate their decision by taking a second look to see if the path they chose was the shortest one
possible.
Multi-Step Procedures –When working on an exercise that requires many different steps, like the last problem
in this section, students sometimes become lost in the process or overwhelmed before they begin. A good way to
ground students, and help them move through the problem, is to create, or have them create, a To-do list. Writing
out the steps that need to be completed will help them understand the process, give them a sense of satisfaction as
the check off parts they have completed, and help them organize their work. Creating the list could be a good group
activity.
Where to Measure? –Now that the students know to measure along a line that is perpendicular to both parallel lines,
they might wonder where along the lines to measure. When working on a coordinate plane it is best to start with a
Chapter 2. Geometry TE - Common Errors