Geometric figure illustrating two adjacent angles at point B, labeled with algebraic expressions (3x + 7)° and (2x + 5)°.

We are given a geometric figure with angles at point $ B $, and we need to solve for $ x $ using the angle expressions provided.

Given:

- Angle $ \angle ABC = (3x + 7)^\circ $
- Angle $ \angle CBD = (2x + 5)^\circ $
- The total angle from $ A $ to $ D $ through $ C $ appears to be a straight line or a full angle at point $ B $, but since points $ A $, $ B $, and $ D $ form a "corner" and $ C $ lies between them, it's likely that $ \angle ABD $ is made up of two adjacent angles: $ \angle ABC $ and $ \angle CBD $.

Let’s assume that $ \angle ABD $ is a straight angle, meaning it measures $ 180^\circ $. This is a common configuration in such problems unless otherwise stated.

So:

$$
\angle ABC + \angle CBD = 180^\circ
$$

Substitute the expressions:

$$
(3x + 7) + (2x + 5) = 180
$$

Simplify:

$$
5x + 12 = 180
$$

Subtract 12 from both sides:

$$
5x = 168
$$

Divide by 5:

$$
x = \frac{168}{5} = 33.6
$$

---

Final Answer:

$$
\boxed{x = 33.6}
$$

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Verification:

Plug back into the angles:

- $ \angle ABC = 3(33.6) + 7 = 100.8 + 7 = 107.8^\circ $
- $ \angle CBD = 2(33.6) + 5 = 67.2 + 5 = 72.2^\circ $
- Sum: $ 107.8 + 72.2 = 180^\circ $ ✔

So the solution is correct.

> Note: If the figure shows that $ \angle ABD $ is not a straight angle (e.g., if it's a right angle or something else), the assumption might change. But based on typical geometry problems and the layout, assuming a straight line at $ B $ (i.e., $ \angle ABD = 180^\circ $) is standard unless specified otherwise.

✔ Therefore, $ \boxed{x = 33.6} $ is the solution.