1. Identify each angle pair. 1. 1 and 3 2. 3 and 6 3. 4 and 5
Warm Up
Identify each angle pair.
1. 1 and 3
2. 3 and 6
3. 4 and 5
4. 6 and 7
corr. s
alt. int. s
alt. ext. s
same-side int s
Why did the parallel lines not recognize each other?

2. Because they had never met
Objective
Prove and use theorems about the angles formed by parallel lines and a transversal.

6. Example 1: Using the Corresponding Angles Postulate
Find each angle measure.
A. mECF
mECF = 70°
B. mDCE
5x = 4x + 22
x = 22
mDCE = 5x
= 5(22)
= 110°

7. Check It Out! Example 1
Find mQRS.
x = 118
mQRS = 180°
Def. of Linear Pair
mQRS =
62°

8. Find the measure of angles 1, 2, 3, and 4.

9. Check It Out! Example 2
Find mABD.
x = 25
mABD = 2(25) + 10 = 60°

10. Example 3: Music Application
Find x and y in the diagram.
By the Alternate Interior Angles
Theorem, (5x + 4y)° = 55°.
By the Corresponding Angles Postulate, (5x + 5y)° = 60°.
5x + 5y = 60
–(5x + 4y = 55)
y = 5
Subtract the first equation from the second equation.
5x + 5(5) = 60
x = 7, y = 5

11. Check It Out! Example 3
Find x and y in the diagram.
By the Alternate Exterior Angles
Theorem, (25x + 5y)° = 125°.
By the Corresponding Angles Postulate, (25x + 4y)° = 120°.
X = 4, y = 5