Question

Ray BD bisects ABC so that DBC=x+8 and ABD=2x-15. What is x?

Answer 1

In the problem, you have a line segment BD that bisects angle ABC. This means that angle ABD is congruent to angle DBC.

So, ABD = DBC.

Given:

DBC = x + 8

ABD = 2x - 15

Now, set up an equation by equating these two expressions:

x + 8 = 2x - 15

Now, solve for x:

Subtract x from both sides:

8 = x - 15

Add 15 to both sides to isolate x:

x = 8 + 15

x = 23

So, the value of x is 23.