try: concepts and connections (27.0821000) yl ic (spring)complementary and supplementary anglesinstruction activeproving the congruent supplements theoremgiven: $\angle 1$ and $\angle 2$ are supplements,$\angle 3$ and $\angle 4$ are supplements,and $\angle 1 \cong \angle 4$.prove: $\angle 2 \cong \angle 3$statements reasons$m\angle 1 = m\angle 4$ $m\angle 2 = m\angle 3$ $m\angle 1 + m\angle 2 = 180$$m\angle 3 + m\angle 4 = 180$ $m\angle 1 + m\angle 2 = m\angle 3 + m\angle 1$ $m\angle 1 + m\angle 2 = m\angle 3 + m\angle 4$statements | reasons1. $\angle 1$ and $\angle 2$ are supp. | 1. given2. $\angle 3$ and $\angle 4$ are supp. | 2. given3. $\angle 1 \cong \angle 4$ | 3. givencorrect! assemble the next statement.

Question

try: concepts and connections (27.0821000) yl ic (spring)complementary and supplementary anglesinstruction  activeproving the congruent supplements theoremgiven: $\angle 1$ and $\angle 2$ are supplements,$\angle 3$ and $\angle 4$ are supplements,and $\angle 1 \cong \angle 4$.prove: $\angle 2 \cong \angle 3$statements reasons$m\angle 1 = m\angle 4$  $m\angle 2 = m\angle 3$  $m\angle 1 + m\angle 2 = 180$$m\angle 3 + m\angle 4 = 180$  $m\angle 1 + m\angle 2 = m\angle 3 + m\angle 1$  $m\angle 1 + m\angle 2 = m\angle 3 + m\angle 4$statements | reasons1. $\angle 1$ and $\angle 2$ are supp. | 1. given2. $\angle 3$ and $\angle 4$ are supp. | 2. given3. $\angle 1 \cong \angle 4$ | 3. givencorrect! assemble the next statement.

Accepted Answer

# Explanation:
## Step1: Define supplementary angles
If two angles are supplements, their measures sum to 180°.
$\boldsymbol{m\angle 1 + m\angle 2 = 180}$
$\boldsymbol{m\angle 3 + m\angle 4 = 180}$
## Step2: Set sums equal to each other
Since both sums equal 180°, they equal each other.
$\boldsymbol{m\angle 1 + m\angle 2 = m\angle 3 + m\angle 4}$
## Step3: Substitute congruent angle measures
Given $\angle 1 \cong \angle 4$, so $m\angle 1 = m\angle 4$. Substitute $m\angle 1$ for $m\angle 4$.
$\boldsymbol{m\angle 1 + m\angle 2 = m\angle 3 + m\angle 1}$
## Step4: Subtract $m\angle1$ from both sides
Cancel $m\angle1$ to isolate remaining angles.
$\boldsymbol{m\angle 2 = m\angle 3}$
## Step5: Conclude angle congruence
If angle measures are equal, angles are congruent.
$\boldsymbol{\angle 2 \cong \angle 3}$

# Answer:
The completed proof steps are:
| Statements | Reasons |
|------------|---------|
| 1. $\angle 1$ and $\angle 2$ are supp. | 1. given |
| 2. $\angle 3$ and $\angle 4$ are supp. | 2. given |
| 3. $\angle 1 \cong \angle 4$ | 3. given |
| 4. $m\angle 1 + m\angle 2 = 180$ | 4. Definition of supplementary angles |
| 5. $m\angle 3 + m\angle 4 = 180$ | 5. Definition of supplementary angles |
| 6. $m\angle 1 + m\angle 2 = m\angle 3 + m\angle 4$ | 6. Transitive property of equality |
| 7. $m\angle 1 = m\angle 4$ | 7. Definition of congruent angles |
| 8. $m\angle 1 + m\angle 2 = m\angle 3 + m\angle 1$ | 8. Substitution property of equality |
| 9. $m\angle 2 = m\angle 3$ | 9. Subtraction property of equality |
| 10. $\angle 2 \cong \angle 3$ | 10. Definition of congruent angles |

The final proven statement is $\boldsymbol{\angle 2 \cong \angle 3}$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Define supplementary angles

Step2: Set sums equal to each other

Step3: Substitute congruent angle measures

Step4: Subtract $m\angle1$ from both sides

Step5: Conclude angle congruence

Answer:

Statements	Reasons
2. $\angle 3$ and $\angle 4$ are supp.	2. given
3. $\angle 1 \cong \angle 4$	3. given
4. $m\angle 1 + m\angle 2 = 180$	4. Definition of supplementary angles
5. $m\angle 3 + m\angle 4 = 180$	5. Definition of supplementary angles
6. $m\angle 1 + m\angle 2 = m\angle 3 + m\angle 4$	6. Transitive property of equality
7. $m\angle 1 = m\angle 4$	7. Definition of congruent angles
8. $m\angle 1 + m\angle 2 = m\angle 3 + m\angle 1$	8. Substitution property of equality
9. $m\angle 2 = m\angle 3$	9. Subtraction property of equality
10. $\angle 2 \cong \angle 3$	10. Definition of congruent angles