In the given figure, XY is a tangent of the circle at point B. AB is the diameter of the circle.

What is the measure of DBE?

since AB is the diameter of the circle.
AEB=90 and ADB=90 ...........(1) [angle formed in the semi-circle]
therefore BDAC
in the triangle BDC;
DBC=180-(BDC+DCB)=180-(90+45)=180-135DBC=45
DBO=OBC-DBC=90-45  [ OBBC, line joining the point of contact to the center is perpendicular to the tangentDBO=45 ........(2)
in the triangle AEB; 
AEB+EBA+BAE=180 [sum of interior angles of a triangle is 180
EBA=180-(AEB+BAE)=180-(90+50)=180-140EBA=40 .........(3)
from eq(2) and eq(3):
DBE=DBO+EBA=45+40=85

hope this helps you

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Wheres the fig??
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