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Then/Now You 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.

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Concept

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**Use Corresponding Angles Postulate**

Example 1 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

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**Use Corresponding Angles Postulate**

Example 1 B. In the figure, m11 = 51. Find m16. Tell which postulates (or theorems) you used. 16 15 Vertical Angles Theorem 15 11 Corresponding Angles Postulate 16 11 Transitive Property () m16 = m11 Definition of congruent angles m16 = 51 Substitution

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**Example 1b B. In the figure, a || b and m18 = 42. Find m25. A. 42**

C. 48 D. 138

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Concept

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Example 2 Use 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

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Example 2 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4. A. 25 B. 55 C. 70 D. 125

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Skills Packet Do #4 - #6

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**Example 3 A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.**

Find Values of Variables Example 3 A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. 5 7 Corresponding Angles Postulate m5 = m7 Definition of congruent angles 2x – 10 = x Substitution x – 10 = 15 Subtract x from each side. x = 25 Add 10 to each side. Answer: x = 25

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**Example 3 B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y.**

Find Values of Variables Example 3 B. ALGEBRA If m4 = 4(y – 25), and m8 = 4y, find y. 8 6 Corresponding Angles Postulate m8 = m6 Definition of congruent angles 4y = m6 Substitution

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**Example 3 m6 + m4 = 180 Supplement Theorem**

Find Values of Variables Example 3 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

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

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Skills Packet Do #7 - #11

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