The statements and reasons why the given statements are true are presented in the following two column proofs;
Question 1
Given: 9·(x + 6) - 41 = 75

Statement                     Reason
 Reason
S1. 9·(x + 6) - 41 = 75    R1. <u>Given</u>
  R1. <u>Given</u>
S2. 9·(x + 6)  =  116         R2. <u>Addition property</u>
R2. <u>Addition property</u>
S3. <u>9·x + 54 = 116 </u>          R3. Distributive property
R3. Distributive property
S4. 9·x = 62                    R4. <u>Subtraction property</u>
R4. <u>Subtraction property</u>
S5.  
                      R5. <u>Division property of equality</u>
 R5. <u>Division property of equality</u>
Question 2.
Statement                                      Reason
        Reason
S1. m∠A + m∠B = m∠D    R1.  Given
                     R1.  Given
S2. ∠C and ∠D form a Linear Pair    R2. Definition of linear pair
   R2. Definition of linear pair
S3. ∠C and ∠D are supplementary    R3. <u>Linear pair ∠s are supplementary</u>
R3. <u>Linear pair ∠s are supplementary</u>
S4. <u>∠C + ∠D = 180° </u>   R4. Definition of supplementary
                           R4. Definition of supplementary
S5. m∠C + m∠A + m∠B = 180°    R5. <u>Substitution property</u>
         R5. <u>Substitution property</u>
Question 3. 
Statement                                      Reason
 Reason
S1. ∠BDA ≅ ∠A                              R1. Given
 R1. Given
S2. ∠BDA ≅ ∠CDE                       R2. <u>Vertical angle theorem</u>
  R2. <u>Vertical angle theorem</u>
S3. ∠CDE ≅ ∠A                       R3. Transitive property of congruency
       R3. Transitive property of congruency
S4. m∠CDE = m∠A                     R4. <u>Definition of congruency</u>
   R4. <u>Definition of congruency</u>
S5. <u>(13·x + 20)° = (14·x + 15)°</u>       R5. Substitution Property of Equality
   R5. Substitution Property of Equality
S6. 14·x° = 13·x + 5°                        R6. <u>Subtraction property</u>
R6. <u>Subtraction property</u>
S7. x = 5                       R7. Subtraction property
                  R7. Subtraction property
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