1. When 2 lines intersect we see 4 individual angles formed.
Chap 2 Sec 4
Vertical Angles and Linear Pairs
When 2 lines intersect we see 4 individual angles formed. 1 2 3 4
We usually talk about these angles 2 at a time. The term we use depends on which 2 angles we are talking about.
If the 2 angles are across from each other (not adjacent), then they are called vertical angles.
If the 2 angles are beside each other (adjacent), then they are called a linear pair. 1

2. Vertical angles are congruent.
Chap 2 Sec 4
Vertical Angles and Linear Pairs 1 2 3 4
Recognizing these angle pairs is important because they have special relationships.
Vertical angles are congruent.
Linear pairs are supplementary (180°). 2

3. Determine whether the labeled angles are vertical angles,
Example 1
Identify Vertical Angles and Linear Pairs
Determine whether the labeled angles are vertical angles,
a linear pair, or neither. b. a. c.
SOLUTION a.
1 and 2 are a linear pair because they are adjacent and their noncommon sides are on the same line. b.
3 and 4 are neither vertical angles nor a linear pair. c.
5 and 6 are vertical angles because they are not adjacent and their sides are formed by two intersecting lines. 3

4. Find the measure of RSU.
Example 2
Use the Linear Pair Postulate
Find the measure of RSU.
SOLUTION
RSU and UST are a linear pair. By the Linear Pair Postulate, they are supplementary. To find mRSU, subtract mUST from 180°.
mRSU = 180° – mUST = 180° – 62° = 118° 4

5. Find the measure of CED.
Example 3
Use the Vertical Angles Theorem
Find the measure of CED.
SOLUTION
AEB and CED are vertical angles. By the Vertical Angles Theorem, CED  AEB, so
mCED = mAEB = 50°. 5

6. Example 4 Find m1, m2, and m3. SOLUTION m2 = 35°
Find Angle Measures
Find m1, m2, and m3.
SOLUTION
m2 = 35°
Vertical Angles Theorem
m1 = 180° – 35° = 145°
Linear Pair Postulate
m3 = m1 = 145°
Vertical Angles Theorem 6

7. Checkpoint Find m1, m2, and m3. 1.
Find Angle Measures
Find m1, m2, and m3. 1.
ANSWER
m1 = 152°; m2 = 28°; m3 = 152° 2.
ANSWER
m1 = 56°; m2 = 124°; m3 = 56° 3.
ANSWER
m1 = 113°; m2 = 67°; m3 = 113°

8. Example 5 Find the value of y. SOLUTION
Use Algebra with Vertical Angles
Find the value of y.
SOLUTION
Because the two expressions are measures of vertical angles, you can write the following equation.
(4y – 42)° = 2y°
Vertical Angles Theorem
4y – 42 – 4y = 2y – 4y
Subtract 4y from each side.
–42 = –2y
Simplify. –2
–42
–2y =
Divide each side by –2.
21 = y
Simplify. 8

9. Find the value of the variable.
Checkpoint
Use Algebra with Angle Measures
Find the value of the variable. 4.
ANSWER 43 5.
ANSWER 16 6.
ANSWER 5