complete the proofs below by filling in the missing statements and reasons.
10. given: ∠1 and ∠2 form a linear pair;
∠1 and ∠3 are supplementary
prove: ∠2 ≅ ∠3

| statements | reasons |
| --- | --- |
| 1. ∠1 and ∠2 form a linear pair | 1. |
| 2. ∠1 and ∠2 are supplementary | 2. |
| 3. m∠1 + m∠2 = 180° | 3. |
| 4. ∠1 and ∠3 are supplementary | 4. |
| 5. m∠1 + m∠3 = 180° | 5. |
| 6. m∠1 + m∠2 = m∠1 + m∠3 | 6. |
| 7. m∠2 = m∠3 | 7. |
| 8. ∠2 ≅ ∠3 | 8. |
© gina wilson (all things algebra), 2014

Question

complete the proofs below by filling in the missing statements and reasons.
10. given: ∠1 and ∠2 form a linear pair;
    ∠1 and ∠3 are supplementary
    prove: ∠2 ≅ ∠3

| statements | reasons |
    | --- | --- |
    | 1. ∠1 and ∠2 form a linear pair | 1.  |
    | 2. ∠1 and ∠2 are supplementary | 2.  |
    | 3. m∠1 + m∠2 = 180° | 3.  |
    | 4. ∠1 and ∠3 are supplementary | 4.  |
    | 5. m∠1 + m∠3 = 180° | 5.  |
    | 6. m∠1 + m∠2 = m∠1 + m∠3 | 6.  |
    | 7. m∠2 = m∠3 | 7.  |
    | 8. ∠2 ≅ ∠3 | 8.  |
    © gina wilson (all things algebra), 2014

Accepted Answer

# Explanation:
## Step1: Identify Given
Statement 1: Given (∠1 and ∠2 form a linear pair)
Reason 1: Given

## Step2: Linear Pair Postulate
Statement 2: ∠1 and ∠2 are supplementary
Reason 2: Linear Pair Postulate (If two angles form a linear pair, they are supplementary)

## Step3: Definition of Supplementary
Statement 3: $ m\angle1 + m\angle2 = 180^\circ $
Reason 3: Definition of Supplementary Angles (Supplementary angles sum to $ 180^\circ $)

## Step4: Identify Given
Statement 4: ∠1 and ∠3 are supplementary
Reason 4: Given

## Step5: Definition of Supplementary
Statement 5: $ m\angle1 + m\angle3 = 180^\circ $
Reason 5: Definition of Supplementary Angles

## Step6: Transitive Property of Equality
Statement 6: $ m\angle1 + m\angle2 = m\angle1 + m\angle3 $
Reason 6: Transitive Property of Equality (Both equal $ 180^\circ $)

## Step7: Subtraction Property of Equality
Statement 7: $ m\angle2 = m\angle3 $
Reason 7: Subtraction Property of Equality (Subtract $ m\angle1 $ from both sides)

## Step8: Definition of Congruent Angles
Statement 8: $ \angle2 \cong \angle3 $
Reason 8: Definition of Congruent Angles (Angles with equal measures are congruent)

# Answer:
| Statements | Reasons |
| --- | --- |
| 1. $ \angle1 $ and $ \angle2 $ form a linear pair | 1. Given |
| 2. $ \angle1 $ and $ \angle2 $ are supplementary | 2. Linear Pair Postulate |
| 3. $ m\angle1 + m\angle2 = 180^\circ $ | 3. Definition of Supplementary Angles |
| 4. $ \angle1 $ and $ \angle3 $ are supplementary | 4. Given |
| 5. $ m\angle1 + m\angle3 = 180^\circ $ | 5. Definition of Supplementary Angles |
| 6. $ m\angle1 + m\angle2 = m\angle1 + m\angle3 $ | 6. Transitive Property of Equality |
| 7. $ m\angle2 = m\angle3 $ | 7. Subtraction Property of Equality |
| 8. $ \angle2 \cong \angle3 $ | 8. Definition of Congruent Angles |

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QUESTION IMAGE

Question

Explanation:

Step1: Identify Given

Step2: Linear Pair Postulate

Step3: Definition of Supplementary

Step4: Identify Given

Step5: Definition of Supplementary

Step6: Transitive Property of Equality

Step7: Subtraction Property of Equality

Step8: Definition of Congruent Angles

Answer:

statements	reasons
2. ∠1 and ∠2 are supplementary	2.
3. m∠1 + m∠2 = 180°	3.
4. ∠1 and ∠3 are supplementary	4.
5. m∠1 + m∠3 = 180°	5.
6. m∠1 + m∠2 = m∠1 + m∠3	6.
7. m∠2 = m∠3	7.
8. ∠2 ≅ ∠3	8.

Statements	Reasons
2. \( \angle1 \) and \( \angle2 \) are supplementary	2. Linear Pair Postulate
3. \( m\angle1 + m\angle2 = 180^\circ \)	3. Definition of Supplementary Angles
4. \( \angle1 \) and \( \angle3 \) are supplementary	4. Given
5. \( m\angle1 + m\angle3 = 180^\circ \)	5. Definition of Supplementary Angles
6. \( m\angle1 + m\angle2 = m\angle1 + m\angle3 \)	6. Transitive Property of Equality
7. \( m\angle2 = m\angle3 \)	7. Subtraction Property of Equality
8. \( \angle2 \cong \angle3 \)	8. Definition of Congruent Angles