Download Lesson 2 - Angles and Parallel Lines

Lesson 3-2
Example 1 Determine Angle Measures
In the figure, m4 = 121. Find m5.
4  7
Corresponding Angles Postulate
7  5
Vertical Angles Theorem
4  5
Transitive Property
m4 = m5
Definition of congruent angles
121 = m5
Substitution
Example 2 Use an Auxiliary Line
Grid-In Test Item
What is the measure of ABC?
Read the Test Item
You need to find mABC. Be sure to identify it
correctly on the figure.
Solve the Test Item
Draw QP through B parallel to m and n.
ABP  DFB
Alternate Interior Angles Theorem
mABP = mDFB
Definition of congruent angles
mABP = 75
Substitution
JBP  EJB
mJBP = mEJB
mJBP = 45
Alternate Interior Angles Theorem
Definition of congruent angles
Substitution
mABC = mABP + mJBP
= 75 + 45 or 120
Angle Addition Postulate
mABP = 75, mJBP = 45
Write each digit of 120 in a column of the grid. Then shade
in the corresponding bubble in each column.
1
2
0
Example 3 Find Values of Variables
ALGEBRA If m1 = 16x - 8, m2 = 4(y + 8),
and m3 = 14x + 2, find x and y.
 Find x.
Since MN ║ PQ , 1  3 by the
Corresponding Angles Postulate.
m1 = m3
Definition of congruent angles
16x - 8 = 14x + 2 Substitution
2x - 8 = 2
Subtract 14x from each side.
2x = 10
Add 8 to each side.
x =5
Divide each side by 2.

Find y.
Since MP ║ NQ , 1  2 by the Alternate Exterior Angles Theorem.
m1 = m2
Definition of congruent angles
16x - 8 = 4(y + 8)
Substitution
16(5) - 8 = 4(y + 8)
x=5
72 = 4y + 32
Simplify.
40 = 4y
Subtract 32 from each side.
10 = y
Divide each side by 4.