SOLUTION: BD bisects angle ABC m angle ABC = 8x m angle ABD = 2x+22 Find m angle DBC (not able to draw angle) options below: _ 11' (degrees) _ 50' _ 44'

Algebra ->  Angles -> SOLUTION: BD bisects angle ABC m angle ABC = 8x m angle ABD = 2x+22 Find m angle DBC (not able to draw angle) options below: _ 11' (degrees) _ 50' _ 44'       Log On


   

Question 601512:
BD bisects angle ABC m angle ABC = 8x m angle ABD = 2x+22 Find m angle DBC
(not able to draw angle)
options below:
_ 11' (degrees)
_ 50'
_ 44'
_ 88'
****This is a REVIEW, with "possible" same question on the test so I'd like to figure it out so then I am prepared if it is. ****
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Since BD bisects ABC, this means that

ABD = (1/2)ABC

or


2ABD = ABC

Plug the expressions in and solve for x

2ABD = ABC

2(2x+22) = 8x

4x+44 = 8x

44 = 8x-4x

44 = 4x

44/4 = x

11 = x

x = 11

Now plug this back into ABD

ABD = 2x+22

ABD = 2(11)+22

ABD = 22+22

ABD = 44

So the measure of angle DBC is 44 degrees (since angle ABD and DBC are equal in measure)