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

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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.

Concept

Use Corresponding Angles Postulate
Example 1 A. In the figure, m11 = 51. Find m15. Tell which postulates (or theorems) you used. What is the relationship between < 11 and < 15? 15  11 Corresponding Angles Postulate m15 = m11 Definition of congruent angles m15 = 51 Substitution m< 15 = 51

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

Example 1b B. In the figure, a || b and m18 = 42. Find m25. A. 42
C. 48 D. 138

Concept

Example 2 Use Theorems about Parallel Lines FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m3. 2  3 Alternate Interior Angles Theorem m2 = m3 Definition of congruent angles 125 = m3 Substitution Answer: m3 = 125

Example 2 FLOOR TILES The diagram represents the floor tiles in Michelle’s house. If m2 = 125, find m4. A. 25 B. 55 C. 70 D. 125

Skills Packet Do #4 - #6

Example 3 A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x.
Find Values of Variables Example 3 A. ALGEBRA If m5 = 2x – 10, and m7 = x + 15, find x. 5  7 Corresponding Angles Postulate m5 = m7 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

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

Example 3 m6 + m4 = 180 Supplement Theorem
Find Values of Variables Example 3 m6 + m4 = 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

Example 3 A. ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find x.

Skills Packet Do #7 - #11

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