请给出这个题目的分析思考及解答---Here is the extracted content from the image: **Problem 4:** 如图1, 已知, AB // CD, 点 E 在 CD 上, 点 G, F 在 AB 上, 点 H 在 AB, CD 之间, 连接 FE, EH, HG, ∠AGH = ∠FED. **(1)求证: HG // EF;** **(2)如图2, FK 平分 ∠AFE 交 CD 于点 K, EH // KF, GM 平分 ∠HGB, ∠KFE : ∠MGH = m : n.** **① 当 m=7, n=3时, 求 ∠GHE 的度数;** **② 如图3, EM 平分 ∠HED, GM 平分 ∠HGB, EM 交 GM 于点 M, 若 ∠GME = 58°, 求 m : n 的值.** --- **Diagram Description:** **图1:** - **Type:** Geometric figure showing two parallel lines cut by transversals. - **Main Elements:** - Two parallel horizontal lines labeled AB (top) and CD (bottom). - Points A, F, G, B are labeled on line AB from left to right. - Point E is labeled on line CD. - Point H is located between lines AB and CD. - Line segments FE, EH, and HG connect the points, forming a polygonal chain. - **Label:** "图1" is placed below the diagram. **图2:** - **Type:** Geometric figure showing two parallel lines cut by transversals and angle bisectors, with a condition of parallel segments. - **Main Elements:** - Two parallel horizontal lines. The top line is labeled A, F, G, B from left to right. The bottom line is labeled C, K, E, D from left to right. - A line segment FK originates from F on AB and intersects CD at K. FK is an angle bisector of ∠AFE. - Point E is on CD. - Point H is between AB and CD. - A line segment EH is drawn. EH is parallel to KF (EH // KF). - A ray or segment GM originates from G on AB. GM is an angle bisector of ∠HGB. - Point M is shown on the segment EH. - **Label:** "图2" is placed below the diagram. **图3:** - **Type:** Geometric figure showing two parallel lines cut by transversals and angle bisectors intersecting at a point. - **Main Elements:** - Two parallel horizontal lines. The top line is labeled A, F, G, B from left to right. The bottom line is labeled C, K, E, D from left to right. - Point E is on CD. - Point H is between AB and CD. - A ray EM originates from E on CD and is the angle bisector of ∠HED. - A ray GM originates from G on AB and is the angle bisector of ∠HGB. - Rays EM and GM intersect at point M. - **Label:** "图3" is placed below the diagram.