Question

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

statements reasons

1. $angle xob cong angle aox$ 1. given
2. $angle xob$ and $angle aox$ are supplementary 2. linear pair theorem
3. $\text{m}angle xob + \text{m}angle aox = 180^circ$ 3. definition of supplementary angles
4. $\text{m}angle xob = \text{m}angle aox$ 4. definition of congruence
5. $2\text{m}angle xob = 180^circ$ 5. substitution property of equality
6. $\text{m}angle xob = 90^circ$ 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 $circ$. using the definition of supplementary angles, $\text{m}angle xob + \text{m}angle aox = 180^circ$. since it is given that $angle xob cong angle aox$, then $\text{m}angle xob = \text{m}angle aox$. applying the $circ$, then $2\text{m}angle xob = 180^circ$. after dividing, $\text{m}angle xob = 90^circ$.

Explanation:

1. The first blank refers to the theorem that states adjacent angles forming a straight line are supplementary, which is the linear pair theorem.
2. The second blank refers to the property that allows replacing an equal quantity with another, which is the substitution property of equality, used here to replace $m\angle AOX$ with $m\angle XOB$ in the supplementary angle equation.

Answer:

First blank: linear pair theorem
Second blank: substitution property of equality