Answer:
Option A
Step-by-step explanation:
angles ABD and DBC are complementary given
angle ABD=50 degrees given
angles ABD and DBC = 90 degrees def. of complementary
angle DBC = 40 degrees algebra (90-50=40)
angles EBF and ABD are vertical angles vertical angles postulate
angle EBF is congruent to angle ABD def. of vertical angles
angle EBF = 50 degrees def. of congruence
angles EBF and ABF are a linear pair def. of linear pair
angles EBF and ABF are supplementary def. of linear pair
angles EBF and ABF = 180 def. of supplementary
angle ABF = 130 degrees algebra (180-50=130)
angles ABF and EBD are vertical angles vertical angles postulate
angles ABF and EBD are congruent def. of vertical angles
angle EBD = 130 degrees def. of congruence
angles CBE + DBC = EBD diagram
angles CBE + DBC = 130 degrees transitive property of congruence
angle ABD = 90 algebra (130-40=90)
B is needed in the process, but the main statement that actually does the justification is A, so option A
