Then/Now You named angle pairs formed by parallel lines and transversals. Use theorems to determine the relationships between specific pairs of angles.

Then/NowYou named angle pairs formed by parallel lines and transversals.

• Use theorems to determine the relationships between specific pairs of angles.

• Use algebra to find angle measurements.

Concept

Example 1Use Corresponding Angles Postulate

A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used.

What is the relationship between < 11 and < 15?

15 11 Corresponding Angles Postulate

m15 = m11 Definition of congruent angles

m15 = 51 Substitution

m< 15 = 51

Example 1

Use Corresponding Angles Postulate

B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used.

16 15 Vertical Angles Theorem

15 11 Corresponding AnglesPostulate

16 11 Transitive Property ()m16 = m11 Definition of congruent

angles

m16 = 51 Substitution

Example 1b

A. 42

B. 84

C. 48

D. 138

B. In the figure, a || b and m18 = 42. Find m25.

Concept

Example 2Use Theorems about Parallel Lines

FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3.

2 3 Alternate Interior Angles Theorem

m2 = m3 Definition of congruent angles

125 = m3 Substitution

Answer: m3 = 125

Example 2

A. 25

B. 55

C. 70

D. 125

FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4.

Skills Packet Do #4 - #6

A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.

Example 3Find Values of Variables

5 7 Corresponding Angles Postulate

m5 = m7 Definition of congruent angles

2x – 10 = x + 15 Substitution

x – 10 = 15 Subtract x from each side.

x = 25 Add 10 to each side.

Answer: x = 25

B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.

Example 3Find Values of Variables

8 6 Corresponding AnglesPostulate

m8 = m6 Definition of congruentangles

4y = m6 Substitution

Example 3Find Values of Variables

m6 + m4 = 180 Supplement Theorem

4y + 4(y – 25) = 180 Substitution

4y + 4y – 100 = 180 Distributive Property

8y = 280 Add 100 to each side.

y = 35 Divide each side by 8.

Answer: y = 35

A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.

Example 3

Skills Packet Do #7 - #11