1. 01/23/17 Warm Up 2.4 On Desk Do the Daily Quiz 2.3

2. ESSENTIAL OBJECTIVE
Calculate Angle Measures of Angles formed by Intersecting Lines

3. VOCABULARY
Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other.

4. Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other.

5. Vertical Angles: two angles that are formed by intersecting lines and are not adjacent to each other.

6. Linear Pair: Two adjacent angles whose opposite rays form a straight line.

7. Linear Pair: Two adjacent angles whose opposite rays form a straight line.

8. 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. b.
3 and 4 are neither. c.
5 and 6 are vertical angles 8

9. Linear Pair Postulate: If two angles form a linear pair, then they are supplementary

10. Find the measure of RSU.
Example 2
Use the Linear Pair Postulate
Find the measure of RSU.
SOLUTION
RSU and UST are supplementary.
To find mRSU, subtract mUST from 180°.
mRSU = 180° – mUST
= 180° – 62° = 118° 10

11. Vertical Angles Theorem
Vertical Angles are Congruent (  )

12. Vertical Angles Theorem
Vertical Angles are Congruent (  )

13. Find the measure of CED.
Example 3
Use the Vertical Angles Theorem
Find the measure of CED.
SOLUTION
AEB and CED are vertical angles.
CED  AEB,
so mCED = mAEB = 50°. 13

14. 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°
m1 = 180° – 35° = 145°
m3 = m1 = 145° 14

15. 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°

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

17. Algebraic expressions are measures of vertical
Example 5
Use Algebra with Vertical Angles
Find the value of y.
SOLUTION
Algebraic expressions
are measures of vertical
angles, you can write the
following equation.
(4y – 42)° = 2y°
4y – 42 – 4y = 2y – 4y
–42 = –2y –2
–42
–2y =
21 = y . 17

18. Review

19. Determine whether the angles are complementary,
supplementary, or neither. Also tell whether the angles are adjacent or nonadjacent. 1. 2.

20. Determine whether the angles are complementary,
supplementary, or neither. Also tell whether the angles are adjacent or nonadjacent. 1.
ANSWER
complementary; adjacent 2.
ANSWER
neither; nonadjacent

21. Find the measures of a complement and a supplement
of the angle. 3.
mR = 27° 4.
mT = 11° 5.
In the figure at the right, ABD and DBC are complementary angles. Find the value of x.

22. Find the measures of a complement and a supplement
of the angle. 3.
mR = 27°
ANSWER
63°; 153° 4.
mT = 11°
ANSWER
79°; 169° 5.
In the figure at the right, ABD and DBC are complementary angles. Find the value of x.
ANSWER
x = 7

23. Hw Worksheet 2.4 B