select the correct answer from each drop - down menu.
given: $ \angle xob \cong \angle aox $
prove: $ m\angle xob=90^{\circ} $

| statements | reasons |
| --- | --- |
| 1. $ \angle xob \cong \angle aox $ | 1. given |
| 2. $ \angle xob $ and $ \angle aox $ are supplementary | 2. linear pair theorem |
| 3. $ m\angle xob+m\angle aox = 180^{\circ} $ | 3. definition of supplementary angles |
| 4. $ m\angle xob=m\angle aox $ | 4. definition of congruence |
| 5. $ 2m\angle xob = 180^{\circ} $ | 5. substitution property of equality |
| 6. $ m\angle xob = 90^{\circ} $ | 6. division property of equality |
write the proof in a paragraph format.
since $ \overline{aob} $ forms a line segment, $ \angle xob $ and $ \angle aox $ are supplementary by the. using the definition of supplementary angles, $ m\angle xob+m\angle aox = 180^{\circ} $. since it is given that $ \angle xob \cong \angle aox $, then $ m\angle xob=m\angle aox $. applying the, then $ 2m\angle xob = 180^{\circ} $. after dividing, $ m\angle xob = 90^{\circ} $.

Question

select the correct answer from each drop - down menu.
given: $ \angle xob \cong \angle aox $
prove: $ m\angle xob=90^{\circ} $

| statements | reasons |
| --- | --- |
| 1. $ \angle xob \cong \angle aox $ | 1. given |
| 2. $ \angle xob $ and $ \angle aox $ are supplementary | 2. linear pair theorem |
| 3. $ m\angle xob+m\angle aox = 180^{\circ} $ | 3. definition of supplementary angles |
| 4. $ m\angle xob=m\angle aox $ | 4. definition of congruence |
| 5. $ 2m\angle xob = 180^{\circ} $ | 5. substitution property of equality |
| 6. $ m\angle xob = 90^{\circ} $ | 6. division property of equality |
write the proof in a paragraph format.
since $ \overline{aob} $ forms a line segment, $ \angle xob $ and $ \angle aox $ are supplementary by the. using the definition of supplementary angles, $ m\angle xob+m\angle aox = 180^{\circ} $. since it is given that $ \angle xob \cong \angle aox $, then $ m\angle xob=m\angle aox $. applying the, then $ 2m\angle xob = 180^{\circ} $. after dividing, $ m\angle xob = 90^{\circ} $.

Accepted Answer

# Brief Explanations:
Since $\overline{AOB}$ forms a line segment, $\angle XOB$ and $\angle AOX$ are supplementary. The linear - pair theorem states that if two angles form a linear pair (they are adjacent and their non - common sides form a straight line), then they are supplementary. So the first blank is filled with "linear pair theorem".

We know that $m\angle XOB + m\angle AOX=180^{\circ}$ and $m\angle XOB = m\angle AOX$ (because $\angle XOB\cong\angle AOX$). Substituting $m\angle AOX$ with $m\angle XOB$ in the equation $m\angle XOB + m\angle AOX = 180^{\circ}$ (using the substitution property of equality: if $a = b$, then $a$ can be substituted for $b$ in an equation). So the second blank is filled with "substitution property of equality".

# Answer:
First blank: linear pair theorem; Second blank: substitution property of equality.

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QUESTION IMAGE

Question

Explanation:

Answer:

statements	reasons
2. \\( \angle xob \\) and \\( \angle aox \\) are supplementary	2. linear pair theorem
3. \\( m\angle xob+m\angle aox = 180^{\circ} \\)	3. definition of supplementary angles
4. \\( m\angle xob=m\angle aox \\)	4. definition of congruence
5. \\( 2m\angle xob = 180^{\circ} \\)	5. substitution property of equality
6. \\( m\angle xob = 90^{\circ} \\)	6. division property of equality