如图，已知AM∥BN，点P是射线AM上一动点（与点A不重合），BC、BD分别平分∠ABP和∠PBN，分别交射线AM于点C，D．（1）①当∠A = 50°时，求∠ABN的度数；②因为AM∥BN，所以∠ACB = ∠CBN；（2）当∠A = x°，求∠CBD的度数（用含x的代数式表示）；（3）当点P运动时，∠ADB与∠APB的度数之比是否随点P的运动而发生变化？若不变化，请求出这个比值；若变化，请写出变化规律；（4）当点P运动到使∠ACB = ∠ABD时，求2∠DBN+\frac{1}{2}∠A的度数。---**Geometric Figure Description:** * **Type:** Geometric figure showing points and lines. * **Lines:** * Line AM: A horizontal line extending to the right from point A, passing through points C, P, and D, and labeled with M at the right end. * Line BN: A horizontal line extending to the right from point B, labeled with N at the right end. Line AM and Line BN appear to be parallel. * Line segment AB: Connects point A and point B. * Line segment BC: Connects point B and point C. * Line segment BP: Connects point B and point P. * Line segment BD: Connects point B and point D. * **Points:** * Point A: Located on the left end of line AM. * Point C: Located on line AM, to the right of A and to the left of P and D. * Point P: Located on line AM, to the right of C and to the left of D. * Point D: Located on line AM, to the right of P. * Point M: Label at the right end of the upper line. * Point B: Located on the left side of line BN. * Point N: Label at the right end of the lower line. * **Relative Position:** * Points A, C, P, D, M are collinear on the upper line. * Points B, N are collinear on the lower line. * The upper line (AM) is above the lower line (BN). * Points C, P, D are between A and M on the upper line. * **Angles:** Angles are formed at point B by the segments BC, BP, and BD. Angles are also formed at points A, C, P, D, and B where lines or segments meet, but no specific angle values or labels for angles are given. **Extracted Text:** * A, C, P, D, M (Labels for points and line) * B, N (Labels for point and line)