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The image shows a geometry problem where BD bisects angle ∠ABC, and we are asked to find the measure of ∠ABC. The given angles are:

- ∠ABD = \( (6x + 16)^\circ \)
- ∠DBC = \( (8x - 23)^\circ \)

Since BD bisects ∠ABC, it means that:

\[
\text{∠ABD} = \text{∠DBC}
\]

So, we can set up the equation:

\[
6x + 16 = 8x - 23
\]

Let's solve for \(x\).The value of \(x\) is \( \frac{39}{2} \) or 19.5.

Now, let's use this value of \(x\) to calculate the measures of ∠ABD and ∠DBC, and then find the full measure of ∠ABC by doubling one of these angles (since ∠ABD = ∠DBC).

BD bisects ∠ABC. Find the measure of ∠ABC given that ∠ABD = (6x + 16)° and ∠DBC = (8x - 23)°.

In this geometry problem, BD bisects angle ∠ABC. Using the given expressions for ∠ABD = (6x + 16)° and ∠DBC = (8x - 23)°, we find the value of x and calculate the measure of ∠ABC. This involves solving linear equations and applying angle bisector principles.

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