1. Deductive Reasoning “The proof is in the pudding.” “Indubitably.” Je solve le crime. Pompt de pompt pompt." Le pompt de pompt le solve de crime!" 2-4 Special Pairs of Angles WE

2. 2-4 Written Exercises Determine the measures of the complements and supplement of each angle. measure sums up to 90 0. 1 Complementary Supplementary 90 – 20 = 70 180 – 10 = 170 2 4 3 90 – 72.5 = 17.5 180 – 72.5 = 107.5 90 – x 180 – x 90 – 2y180 – 2y

3. 5 6 2 complementary angles are congruent. Find their measures. x + x = 90 2x = 90 x = 45 45 0 and 45 0 2 supplementary angles are congruent. Find their measures. x + x = 180 2x = 180 x = 90 90 0 and 90 0

4. Name another right angle. 7 In the diagram, is a right angle. Name the angles.

5. Two complementary angles. 8 Name the angles.

6. Two congruent supplementary angles. 9 Name the angles.

7. Two noncongruent supplementary angles. 10 Name the angles.

8. Two noncongruent supplementary angles. 10 Name the angles.

9. Two acute vertical angles. 11 Name the angles.

10. Two obtuse vertical angles. 12 Name the angles.

11. Vertical Angle Th. Z Y X W V U T S In the diagram, bisects and Label completely ! Vertical Angle Th. 35 Vertical Angle Th. 120 60 60+60+35+x = 180 x = 25 25 35 Vertical Angle Th. Now you answer the questions. O

12. Z Y X W V U T S In the diagram, bisects and 35 60 25 35 14 13 35 155 O

13. Z Y X W V U T S In the diagram, bisects and 35 60 25 35 16 15 25 120 O

14. Z Y X W V U T S In the diagram, bisects and 35 60 25 35 18 17 60 85 O

15. 19 (3x-5) 70 3x -5 = 70 3x = 75 x = 25 divide by 3 Vertical Angles

16. 20 (3x+8) (6x-22) 3x + 8 = 6x - 22 3x + 30 = 6x 30 = 3x 10 = x divide by 3 Vertical Angles

17. 21 4x 64 36 Vertical Angles 4x = 64 + 36 4x = 100 X = 25 Divide by 4

18. 22 are supplements a] If, find. 214 3 27 180 – 27 = 153

19. 22 are supplements b] If, find. 214 3 xx 180 – x

20. 22 are supplements c] If 2 angles are congruent, must their supplements be congruent? 214 3 xx YES ! y y

21. 23 Given: Prove: Label completely first. 1 23 4 gg ? ? Statements Reasons Note the flow is better without the given first. Transitive Prop. Of Equality Vert. Angles are congruent Given Vert. Angles are congruent

22. 24 If and are supplementary, Then find the values of x, and. Start with a labeled diagram. AB 2x x - 15 2x + x – 15 = 180 3x – 15 = 180 3x = 195 x = 65 Divide by 3 A = 2(65) A = 130 B = 65 - 15 B = 50

23. 25 If and are supplementary, Then find the values of x, and. Start with a labeled diagram. AB X + 16 2x - 16 X + 16 +2x– 16 = 180 x = 60 Divide by 3 A = 60 + 16 A = 76 B = 2(60) - 16 B = 120 - 16 3x = 180 B = 104

24. 26 If and are complementary, Then find the values of y, and. Start with a labeled diagram. C D 3y+5 2y 3y + 5 + 2y = 90 5y + 5 = 90 5y = 85 y = 17 divide by 5 C = 3(17) + 5 C = 51 + 5 C = 56 D = 2(17) D = 34

25. 27 If and are complementary, Then find the values of y, and. Start with a labeled diagram. C D y - 8 3y + 2 y – 8 + 3y + 2 = 90 4y - 6 = 90 4y = 96 y = 24 divide by 4 C = 24 - 8 C = 16 D = 3(24) + 2 D = 72 + 2 D = 74

26. 28 Use the information to find an equation and solve. Find the measure of an angle that is twice as large as its supplement. 2( ) x = 180 – x x = 180 – 2x 3x = 180 x = 60 180 – 60 = 120

27. 29 Use the information to find an equation and solve. Find the measure of an angle that is half as large as its complement. x = 90 - x Multipy by 2 to get rid of fractions 2 2 2x = 90 - x 3x = 90 x = 30 90 – 30 = 60

28. 30 Use the information to find an equation and solve. The measure of a supplement of an angle is 12 more than twice the measure of the angle. 180 – x = 12 + 2x 180 = 12 + 3x 168 = 3x 56 = x 180 – 56 = 124

29. 31 Use the information to find an equation and solve. A supplement of an angle is six times as large as the complement of the angle. 180 – x =6( ) 90 - x 180 – x = 540 – 6x 180 + 5x = 540 5x = 360 x = 72 Supplement 180 – 72 = 108 Complement 90 – 72 = 18

30. 32 Find the values of x and y. x (2y – 17) (3x – 8) x + 3x – 8 = 180 4x – 8 = 180 4x = 188 x = 47 47 47 + 2y – 17 = 180 2y + 30 = 180 2y = 150 y = 75

31. 33 Find the values of x and y. 50 x 3x - y 2x - 16 2x – 16 = 50 2x = 66 x = 33 33 33 = 3(33) - y 33 = 99 - y - 66 = - y 66 = y

32. C’est fini. Good day and good luck.