Notice that
[tex]\angle BOM\cong\angle DON[/tex]Because they are vertical angles, and
[tex]\angle AOM\cong\angle DON[/tex]is a given congruence.
Therefore, we can conclude that
[tex]\angle AOM\cong\angle BOM[/tex]Because they are congruent to the same angle: Angle DON.
Therefore, the correct answer is Option D.