Suppose O lies on the interior of <ABC, D lies on the interior of <ABO and E lies on the interior of < OBC.
It is also given that m<DBO = m<EBC and m<ABC = 120, m<DBC = 90.
What is the relationships between <DBE and <OBC ?
From the information in the problem we obtain the following drawing.
m<DBE = m<OBC.
Notice this in the following diagram
Since m<ABC = 120 and m<DBC = 90, m<ABD = 30.
We know this from the angle addition postulate, m<ABD + m<DBC = m<ABC.