1. Lesson 4
Lines & Angles
Vertical Angles

2. Warm-Up
N and M are complementary. The measure of M is 83º. Find the measure of N.
Find the value of x.
Write the angle measures of a pair of supplementary angles. How do you know your angle measures are supplementary?

3. Target: Understand and apply the properties of vertical angles.

4. Vocabulary Vertical Angles: Nonadjacent angles formed by two
intersecting lines.
Linear Pair: Two adjacent angles whose non-common
sides are opposite rays.

5. Angle Relationships Vertical angles are equal in measure.
If two angles form a linear pair, they are supplementary angles.

7. Example 1 Find the measure of each missing angle. a. m3
Vertical angles are congruent. m2 = m3
54° = m3
b. m1
m1 and m2 are a linear pair. m1 + m2 = 180
Substitute known values m = 180
Subtract 54 from each side –54 –54
m1 = 126°
c. m4
Vertical angles are congruent. m1 = m4
126° = m4

8. Example 2
Use the diagram to the right. a. Solve for x. b. Find the measure of each angle. a. Vertical angles have equal measures. 3x + 7 = x + 30 Subtract x from each side. –x –x 2x + 7 = 30 Subtract 7 from each side. –7 –7 2x = 23 Divide by 2 on each side. 2 2 x = 11.5 b. Substitute the solution for x in each angle expression. (3x + 7) = (3(11.5) + 7) = ( ) = 41.5° (x + 30) = ( ) = 41.5° The measure of each angle is 41.5°.

9. Exit Problems
Find the value of x.

10. Communication Prompt
Why do you think equation-solving is one of the most important mathematical skills?