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 supplementary angles, m∠xob + m∠aox = 180°. since it is given that ∠xob≅∠aox. applying the

Explanation:

Step1: Given congruent angles

$\angle XOB\cong\angle AOX$ (Given)

Step2: Identify supplementary - angle relationship

$\angle XOB$ and $\angle AOX$ are supplementary because they form a linear - pair (Linear pair theorem)

Step3: Write the sum of supplementary angles

$m\angle XOB + m\angle AOX=180^{\circ}$ (Definition of supplementary angles)

Step4: Use the definition of congruence

Since $\angle XOB\cong\angle AOX$, then $m\angle XOB = m\angle AOX$ (Definition of congruence)

Step5: Substitute equal angles

Substitute $m\angle AOX$ with $m\angle XOB$ in $m\angle XOB + m\angle AOX = 180^{\circ}$, we get $2m\angle XOB=180^{\circ}$ (Substitution property of equality)

Step6: Solve for $m\angle XOB$

Divide both sides of $2m\angle XOB = 180^{\circ}$ by 2, $m\angle XOB = 90^{\circ}$ (Division property of equality)

Answer:

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