Answer:
AB is 24
Step-by-step explanation:
Using the segment addition postulate, AC = AB+BC.
We know that BD=BC, BD=5x-26 and BC=2x+1. So set up an equation to find the value of x:
5x-26=2x+1
Subtract 2x from each side:
5x-26-2x = 2x+1-2x
3x-26 = 1
Add 26 to each side:
3x-26+26 = 1+26
3x=27
Divide both sides by 3:
3x/3 = 27/3
x = 9
This means that BC = 2x+1 = 2(9)+1 = 18+1 = 19.
We know that AC = AB+BC; using our given information as well as the value of BC we just found, we have
43 = AB+19
Subtract 19 from each side:
43-19 = AB+19-19
24 = AB
