Based on the given nomenclature of angles, I think the illustration would look like that shown in the attached picture. The common vertex is point B, that's why the middle point of the given angles is B. Now, according to Angle Addition Postulate, the individual interior angles should sum up to the total angle. So, the equation would be
m∠ABD = m∠ABC + m∠CBD
m∠ABC = m∠ABD - m∠CBD
m∠ABC = 85° - m∠CBD
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