We have completed the proof by applying the linear pair theorem and the substitution property of equality
Proofs of angles
From the question, we are to complete the proof
Since AOB forms a line segment, ∠XOB and ∠AOX are supplementary by the Linear pair theorem
NOTE: The linear pair theorem states that, if two angles form a linear pair, then the measures of the angles add up to 180°. That is they are supplementary
Also,
Since it is given that ∠XOB ≅ ∠AOX, then m ∠XOB = m ∠AOX. Applying the substitution property of equality, then 2m ∠XOB = 180°. After dividing, m ∠XOB = 90°.
Hence, the measure of angles ∠XOB (m ∠XOB ) is 90°
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