1.Using the figure on the right, classify the relationship between <1 and <4 2.Using the figure on the right, find the measure of each angle. m<9 = 2x – 4 m<10 = 2x +4 PROBLEMS OF THE DAY/HOMEWORK QUIZ! n m p 10 9

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. 3.2 Angles and Parallel Lines

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

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

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

Example 3 Find Values of Variables m  6 + m  4=180Supplement Theorem 4y + 4(y – 25)=180Substitution 4y + 4y – 100=180Distributive Property 8y=280Add 100 to each side. y=35Divide each side by 8. Answer: y = 35

In summary, When you have parallel lines and a transversal, you will have -Congruent corresponding angles -Congruent alternate interior angles -Congruent alternate exterior angles -Supplementary consecutive angles -Congruent vertical angles **These are always congruent You can use these “facts” to solve for unknown angles and values of x!