Final answer:
To find the value of x, we can use the Angle Bisector Theorem. The value of x is (bc + 10)/7.
Step-by-step explanation:
In order to find the value of x, we can use the Angle Bisector Theorem.
According to the theorem, if a line bisects an angle, it divides the opposite side into two segments that are proportional to the other two sides of the triangle.
In this case, since bd bisects the angle into abd and dbc, we can set up the following proportion: ab/bc = ad/dc.
Using the given measures, we have:
(7x-10)/bc = ad/dc.
Since ad = dc (because bd bisects the angle), we can simplify the equation:
(7x-10)/bc = 1.
Cross multiplying, we get:
7x-10 = bc.
From here, we can solve for x:
7x = bc + 10.
x = (bc + 10)/7.
This is the value of x.