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To solve this problem, let's first analyze the given information:

We have a triangle \( ABC \) with a point \( D \) on line segment \( AC \), creating two smaller triangles, \( ABD \) and \( BDC \).

We are asked to find the relationship between the angles \( \angle ACB - \angle ABC \) and \( \angle ADB \).

### Analysis:
1. In triangle \( ABC \), the sum of angles is:
   \[
   \angle ABC + \angle BAC + \angle ACB = 180^\circ
   \]
   
2. Similarly, in triangle \( ABD \), the sum of angles is:
   \[
   \angle ABD + \angle ADB + \angle BAD = 180^\circ
   \]

From the given options, the problem appears to involve an exploration of angle relationships and possibly the use of properties like exterior angles or congruency/similarity of triangles.

### Checking the options:
- **Option A:** \( \angle BAC = \angle ABC \) – This doesn't seem relevant here.
- **Option B:** \( \frac{AB}{AD} = \frac{AC}{AD} \) – This represents a ratio and is unrelated to angles.
- **Option C:** \( \triangle ABC = \triangle DAB \) – Both have dissimilar congruency factors.
The答案

In the given figure, ∠ACB - ∠ABC = ∠ADB. The correct option is?

Learn how to solve the geometry problem where ∠ACB - ∠ABC = ∠ADB, using angle properties in triangles and the Exterior Angle Theorem. This detailed explanation is suitable for Grades 8-10 and covers key concepts in triangle geometry.

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