Lesson 3-2

Example 1  Determine Angle Measures
In the figure, m4 = 121. Find m5.	
	4	 7	Corresponding Angles Postulate
	7	 5	Vertical Angles Theorem
	4	 5	Transitive Property
	m4	= m5	Definition of congruent angles
	121	= m5	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 mABC. Be sure to identify it correctly on the figure.

Solve the Test Item
Draw  through B parallel to m and n.	
	ABP	 DFB	Alternate Interior Angles Theorem
	mABP	= mDFB	Definition of congruent angles
	mABP	= 75	Substitution

1

2

0

	JBP	 EJB	Alternate Interior Angles Theorem
	mJBP	= mEJB	Definition of congruent angles
	mJBP	= 45	Substitution

mABC	= mABP + mJBP	Angle Addition Postulate
	= 75 + 45 or 120	mABP = 75, mJBP = 45

Write each digit of 120 in a column of the grid. Then shade 	
in the corresponding bubble in each column. 

Example 3  Find Values of Variables
ALGEBRA  If m1 = 16x - 8, m2 = 4(y + 8), 	
and m3 = 14x + 2, find x and y.
•	Find x.
Since ║, 1  3 by the
Corresponding Angles Postulate.
	m1	= m3	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 ║, 1  2 by the Alternate Exterior Angles Theorem.
	m1	= m2	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.