Practice and Problem-Solving Exercises A Practice Find the value of each variable. See Problems 1. Find the measures of the labeled angles In each exercise. 9. Exercise 6 10. Exercise 7 11. Exercise 8 12. Developing Proof Complete the following proof by filling in the blanks. see Problem 2 Given: 21 = 23 Prove: 26 - 44 Statements Reasons 1) 1) Given 2)13. Developing Proof Fill in the blanks to complete this proof of See Problem 3. the Congruent Complements Theorem (Theorem 2-3). If two angles are complements of the same angle, then the two angles are congruent. Given: 21 and 42 are complementary. 23 and Z2 are complementary. Prove: 21 9 23 Proof: 21 and 42 are complementary and 23 and Z2 are complementary because it is given. By the definition of complementary angles, m21 + m/2 - a. ? and m/3+ m/2 - b. ? . Then m/1 + m/2= m/3 + m/2 by the Transitive Property of Equality. Subtract m42 from each side. By the Subtraction Property of Equality, you get m21 = c. ? . Angles with the same measure are d. ? , so 21 = 23. 14. Think About a Plan What is the measure of the angle formed by Park St. and 116th St.? . Can you make a connection between the angle you 15 141911 Elm St Main St need to find and the labeled angle? . How are angles that form a right angle related? 15. Open-Ended Give an example of vertical angles in your Park St. home or classroom. Algebra Find the value of each variable and the measure of each labeled angle. 16. 17. (x + 10] (4x - 35) (3x + 8)