请回答以上问题，并详细说明解答技巧。---```text
例 3. 如图 1, 在三角形 ABC 中, ∠ABC=90°, 直线 a 与边 AC, AB 分别交于 D, E 两点, 直线 b 与边 BC, AC 分别交于 F, G 两点, 且 a//b.
**Chart/Diagram Description:**
**图1:**
* Type: Geometric figure.
* Elements:
* Triangle ABC with a right angle at vertex B.
* Horizontal line 'a' intersecting side AC at point D and side AB at point E.
* Horizontal line 'b' below line 'a', parallel to line 'a'. Line 'b' intersects side BC at point F and side AC at point G.
* Labels: A, B, C, D, E, F, G, a, b.
* Annotation: "图1" below the figure.
**图2:**
* Type: Geometric figure.
* Elements:
* Similar to Figure 1, with triangle ABC (right angle at B), line 'a' intersecting AC at D and AB at E, and line 'b' (parallel to 'a') intersecting BC at F and AC at G.
* Additional point P is located on side AB.
* Line segment PF connects points P and F.
* Labels: A, B, C, D, E, F, G, P, a, b.
* Annotation: "图2" below the figure.
**图3:**
* Type: Geometric figure.
* Elements:
* Similar to Figure 1, with triangle ABC (right angle at B), line 'a' intersecting AC at D and AB at E, and line 'b' (parallel to 'a') intersecting BC at F and AC at G.
* The line AB is extended to intersect line 'b' at point Q.
* Ray DC is extended.
* Point M is a movable point on the extended ray from D through C (ray DC).
* Line segments ME and MQ are drawn.
* Labels: A, B, C, D, E, F, G, Q, M, a, b.
* Annotation: "图3" below the figure.
**Extraction Content:**
(1) 若∠AED=40°, 求∠BFG 的度数;
(2) 如图 2, P 为边 AB 上一点, 连接 PF, 若∠PFG+∠BFG=180°, 探究∠PFG 与∠AED 的数量关系, 并说明理由
(3) 如图 3, 若∠AED=m, 延长 AB 交直线 b 于点 Q, 在射线 DC 上有一动点 M, 连接 ME, MQ, 请写出∠MEQ、∠EMQ、∠MQF 之间的数量关系 (用 m 的代数式表示)。
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