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

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

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

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

Two complementary angles. 8 Name the angles.

Two congruent supplementary angles. 9 Name the angles.

Two noncongruent supplementary angles. 10 Name the angles.

Two noncongruent supplementary angles. 10 Name the angles.

Two acute vertical angles. 11 Name the angles.

Two obtuse vertical angles. 12 Name the angles.

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 x = 180 x = Vertical Angle Th. Now you answer the questions. O

Z Y X W V U T S In the diagram, bisects and O

Z Y X W V U T S In the diagram, bisects and O

Z Y X W V U T S In the diagram, bisects and O

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

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

21 4x Vertical Angles 4x = x = 100 X = 25 Divide by 4

22 are supplements a] If, find – 27 = 153

22 are supplements b] If, find xx 180 – x

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

23 Given: Prove: Label completely first 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

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

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

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

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 = C = 16 D = 3(24) + 2 D = D = 74

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 = 120

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 = 60

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 = x 180 = x 168 = 3x 56 = x 180 – 56 = 124

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 x = 540 5x = 360 x = 72 Supplement 180 – 72 = 108 Complement 90 – 72 = 18

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

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

C’est fini. Good day and good luck.