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The image presents a geometry problem involving a quadrilateral. Based on the diagram, we are given:

- \( AD \parallel BC \)
- \( AD = 9 \, \text{cm} \)
- \( BC = 12 \, \text{cm} \)
- \( \angle ABC = 46^\circ \)
- \( \angle BAC = 57^\circ \)
- \( AC \) is an unknown length to be found in part (a), and \( CD \) in part (b).

Let me break down how we can approach this problem:

1. **For part (a) finding \( AC \):**
   - The triangle \( ABC \) is described with known angles and one known side, \( BC = 12 \, \text{cm} \). This allows us to apply the **Law of Sines**:
     \[
     \frac{AC}{\sin(\angle ABC)} = \frac{BC}{\sin(\angle BAC)}
     \]

2. **For part (b) finding \( CD \):**
  

Given that AD is parallel to BC, AD = 9 cm, BC = 12 cm, ∠ABC = 46°, and ∠BAC = 57°, solve for AC and CD.

Learn how to solve a geometry problem involving a quadrilateral where AD is parallel to BC, with angles and side lengths provided. This problem uses the Law of Sines to find the unknown sides AC and CD. Suitable for students in Grades 9-12.

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