Question

select the correct answer from each drop - down menu. given: ∠xob≅∠aox prove: m∠xob = 90°. statements reasons 1. ∠xob≅∠aox 1. given 2. ∠xob and ∠aox are supplementary 2. linear pair theorem 3. m∠xob + m∠aox = 180° 3. definition of supplementary angles 4. m∠xob = m∠aox 4. definition of congruence 5. 2m∠xob = 180° 5. substitution property of equality 6. m∠xob = 90° 6. division property of equality write the proof in a paragraph format. since aob forms a line segment, ∠xob and ∠aox are supplementary by the m∠xob + m∠aox = 180°. since it is given that ∠xob≅∠aox, then m∠xob = m∠aox. applying the using the definition of supplementary angles, 2m∠xob = 180°. after dividing, m∠xob = 90°.

Explanation:

Step1: Recall linear - pair property

Since $\angle XOB$ and $\angle AOX$ form a linear - pair (because $AOB$ is a line segment), by the linear - pair theorem, they are supplementary. So $m\angle XOB + m\angle AOX=180^{\circ}$.

Step2: Use congruence definition

Given that $\angle XOB\cong\angle AOX$, by the definition of congruent angles, $m\angle XOB = m\angle AOX$.

Step3: Substitute

Substitute $m\angle AOX$ with $m\angle XOB$ in the equation $m\angle XOB + m\angle AOX = 180^{\circ}$. We get $m\angle XOB+m\angle XOB = 180^{\circ}$, which simplifies to $2m\angle XOB=180^{\circ}$.

Step4: Solve for $m\angle XOB$

Divide both sides of the equation $2m\angle XOB = 180^{\circ}$ by 2. Using the division property of equality, we have $m\angle XOB=\frac{180^{\circ}}{2}=90^{\circ}$.

Answer:

$m\angle XOB = 90^{\circ}$