请帮我解答这道初中几何题---**Question 4** **Question Stem:** 4. 如图 2-ZT-5, 已知∠1=∠2, ∠3=∠4, 判断∠A, ∠C 与∠E 之间的数量关系, 并证明你的结论. **Translation of Question Stem:** 4. As shown in Figure 2-ZT-5, given ∠1=∠2 and ∠3=∠4, determine the quantitative relationship between ∠A, ∠C, and ∠E, and prove your conclusion. **Chart/Diagram Description:** * **Type:** Geometric figure, specifically a complex polygon (appears to be a five-pointed star or a pentagon with internal lines). * **Main Elements:** * **Points:** Five labeled vertices: A, B, C, D, E. * **Lines/Segments:** * Outer boundary segments: AB, BD, DC, CE, EA. These segments form a closed polygon ABCDE. * Internal diagonal segments: AC and BE. * Two additional internal line segments related to the angles: Let X be the intersection point of diagonal AC and diagonal BD. Let Y be the intersection point of diagonal BE and segment CD. * The line segment from B passing through X (BX) is shown. * The line segment from D passing through Y (DY) is shown. * **Angles:** * Angles to be related: ∠A, ∠C, ∠E (these are internal angles of the polygon ABCDE at vertices A, C, and E respectively). * Given angles: * ∠1 and ∠2 are angles at vertex B. Specifically, ∠1 is the angle ∠ABX and ∠2 is the angle ∠XBD, where X is the intersection of AC and BD. * ∠3 and ∠4 are angles at vertex D. Specifically, ∠3 is the angle ∠BDY and ∠4 is the angle ∠YDC, where Y is the intersection of BE and CD. * **Relative Position and Direction:** * Point A is at the top. * Point B is to the right of A. * Point D is below B and to its right. * Point C is below D and to its left. * Point E is to the left of C and somewhat below A. * The line segment AC passes through the interior of the figure, connecting A to C. * The line segment BE passes through the interior of the figure, connecting B to E. * The line segment BX (where X is on AC and BD) divides ∠ABD into ∠1 and ∠2. * The line segment DY (where Y is on BE and CD) divides ∠BDC into ∠3 and ∠4. * **Labels and Annotations:** The figure is labeled "图 2-ZT-5" (Figure 2-ZT-5).