Question

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

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

write the proof in a paragraph format.
since $\overline{aob}$ forms a line segment, $\angle xob$ and $\angle aox$ are supplementary by the \\(\boldsymbol{\text{drop - down 1}}\\). 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 \\(\boldsymbol{\text{drop - down 2}}\\), then $2m\angle xob = 180^{circ}$. after dividing, $m\angle xob = 90^{circ}$.
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Explanation:

For the first drop - down: The reason why ∠XOB and ∠AOX are supplementary when \(\overline{AOB}\) is a line segment is the linear pair theorem. A linear pair of angles is formed when two adjacent angles form a straight line, and they are supplementary.
For the second drop - down: After we know that \(m\angle XOB=m\angle AOX\) and \(m\angle XOB + m\angle AOX = 180^{\circ}\), we substitute \(m\angle AOX\) with \(m\angle XOB\) (since they are equal) to get \(2m\angle XOB=180^{\circ}\). This is the substitution property of equality, which allows us to replace one equal quantity with another in an equation.

Answer:

First drop - down: linear pair theorem
Second drop - down: substitution property of equality