BD bisects ABC, DBC=10x, ABD=4x+15 . Find DBC

Question

BD bisects ABC, DBC=10x, ABD=4x+15 . Find DBC

Answer 1

Draw a diagram and label!

BD bisects ∠ABC              given

∠ABD = ∠CBD                 definition of bisect

4x + 15 = 10x                substitution

15 = 6x                          subtract 4x from both sides

15/6 = x                         divide both sides by 6

5/2 = x                          reduce

 

∠DBC = 10x

∠DBC = 10(5/2)

∠DBC = 25