Question 1179598
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**1. Given: 𝑚∠1 = 90°; ∠1 ≅ ∠2
   Prove: ∠2 is a right angle**

   **Proof:**

   | Statement | Reason |
   |---|---|
   | 1. 𝑚∠1 = 90° | Given |
   | 2. ∠1 ≅ ∠2 | Given |
   | 3. 𝑚∠1 = 𝑚∠2 | Definition of congruent angles (If angles are congruent, their measures are equal) |
   | 4. 𝑚∠2 = 90° | Substitution Property of Equality (Substitute 90° for 𝑚∠1 in step 3) |
   | 5. ∠2 is a right angle | Definition of a right angle (An angle with a measure of 90° is a right angle) |

**2. Given: 3(x + 1) = 6(x - 3)
   Prove: x = 7**

   **Proof:**

   | Statement | Reason |
   |---|---|
   | 1. 3(x + 1) = 6(x - 3) | Given |
   | 2. 3x + 3 = 6x - 18 | Distributive Property (Multiply through the parentheses) |
   | 3. 3x + 21 = 6x | Addition Property of Equality (Add 18 to both sides) |
   | 4. 21 = 3x | Subtraction Property of Equality (Subtract 3x from both sides) |
   | 5. 7 = x | Division Property of Equality (Divide both sides by 3) |
   | 6. x = 7 | Symmetric Property of Equality (If a = b, then b = a) |

**3. Given: 𝑚∠1 = 180°; ∠1 ≅ ∠2; 𝑚∠2 ≅ 𝑚∠3
   Prove: ∠3 is a straight angle**

   **Proof:**

   | Statement | Reason |
   |---|---|
   | 1. 𝑚∠1 = 180° | Given |
   | 2. ∠1 ≅ ∠2 | Given |
   | 3. 𝑚∠1 = 𝑚∠2 | Definition of congruent angles |
   | 4. 𝑚∠2 = 180° | Substitution Property of Equality (Substitute 180° for 𝑚∠1 in step 3) |
   | 5. 𝑚∠2 ≅ 𝑚∠3 | Given |
   | 6. 𝑚∠2 = 𝑚∠3 | Definition of congruent angles |
   | 7. 𝑚∠3 = 180° | Substitution Property of Equality (Substitute 180° for 𝑚∠2 in step 6) |
   | 8. ∠3 is a straight angle | Definition of a straight angle (An angle with a measure of 180° is a straight angle) |

**4. Given: 8.5s - 81.7 = -9.23s + 148.79
   Prove: s = 13**

   **Proof:**

   | Statement | Reason |
   |---|---|
   | 1. 8.5s - 81.7 = -9.23s + 148.79 | Given |
   | 2. 17.73s - 81.7 = 148.79 | Addition Property of Equality (Add 9.23s to both sides) |
   | 3. 17.73s = 230.49 | Addition Property of Equality (Add 81.7 to both sides) |
   | 4. s = 13 | Division Property of Equality (Divide both sides by 17.73) |