Answer: 105 °.
Your question is incomplete. Searching on internet I could complete the statement and find the figure.
1) Statement:
- segment AB = segment BC
- angle BDC = 37.5 °
- find angle CBD.
2) Figure: see file attached.
3) Analysis:
3.1) Triangle ABD has angles equal to 60°, so the third angle has to be 60° and the triangle is equilateral (all the three sides are equal).
3.2) As you are told that segment AC = segment BC, and you have found that segment DB = segment AB, by transitivity you conclude that segment DB = segment BC.
3.3) That two sides of triangle BDC are congruent means it is isosceles and that the two angles opposite to angle BDC are equal.
3.4) Then the measure of the angle CBD is 180° - 37.5° - 37.5° = 105°.
That is the answer: angle CBD is 105°.