Ray BD bisects ∠ABC so that m∠DBC = x + 8 and

m∠ABD = 2x − 15. What is x?

Ray BD bisects ∠ABC

That means the two angles formed are congruent.
That means their measures are equal. So,
x+8 = 2x-15
Now just find x.

since everyone else won't answer it, I will. x = 13

thank. you somesh the answer was 13

i got 23?

To find the value of x, we can use the fact that the sum of angles in a triangle is always 180 degrees.

Given that Ray BD bisects ∠ABC, we know that ∠ABD and ∠DBC are equal. Let's set them equal to each other and solve for x.

m∠ABD = 2x - 15
m∠DBC = x + 8

Since ∠ABD = ∠DBC, we can set up an equation:
2x - 15 = x + 8

Now, let's solve for x.

2x - x = 8 + 15
x = 23

So, x = 23.

"bisect" means to cut into two equal parts, so

2x-15 = x+8

just solve this trivial equation for x