∠XOB and ∠AOX are supplementary by the definition of supplementary angles.
Applying the substitution property of equality, then 2m ∠XOB = 180°
The blanks have been filled and the proof has been completed.
Proof of angles
From the question, we are to fill in the blanks to complete the proof
The proof can be completed as shown below
Since AOB forms a line segment, ∠XOB and ∠AOX are supplementary by the definition of supplementary angles. Using the definition of supplementary angles m ∠XOB + m ∠AOX = 180°. 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°.
The blanks have been filled and hence, the proof has been completed.
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