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