答案：3.解:(1)$∠ M+∠ N=180°$.理由如下:
$\because EF// BC$,$\therefore ∠ ADF=∠ ABC$.
$\because BM$是$∠ ABC$的平分线,$DN$是$∠ ADF$的平分线,
$\therefore ∠ ABM=\frac{1}{2}∠ ABC$,$∠ ADN=\frac{1}{2}∠ ADF$,
$\therefore ∠ ABM=∠ ADN$,$\therefore DN// BM$,$\therefore ∠ M+∠ N=180°$.
(2)$∠ M=∠ N$.理由如下:
$\because EF// BC$,$\therefore ∠ ABC=∠ BDE$.
$\because BM$是$∠ ABC$的平分线,$DN$是$∠ BDE$的平分线,
$\therefore ∠ ABM=\frac{1}{2}∠ ABC$,$∠ BDN=\frac{1}{2}∠ BDE$,
$\therefore ∠ ABM=∠ BDN$,$\therefore BM// DN$,$\therefore ∠ M=∠ N$.
(3)如图,延长$ND,BM$交于点$G$.
$\because EF// BC$,
$\therefore ∠ BDF+∠ ABC=180°$.
$\because DN$是$∠ ADE$的平分线,
$\therefore ∠ ADN=\frac{1}{2}∠ ADE$.
$\because ∠ ADN=∠ BDG$,$∠ ADE=∠ BDF$,
$\therefore ∠ BDG=\frac{1}{2}∠ BDF$.
$\because BM$是$∠ ABC$的平分线,
$\therefore ∠ ABM=\frac{1}{2}∠ ABC$,
$\therefore ∠ BDG+∠ ABM=\frac{1}{2}∠ BDF+\frac{1}{2}∠ ABC=\frac{1}{2}(∠ BDF+$
$∠ ABC)=\frac{1}{2}× 180°=90°$,
$\therefore ∠ G=180°-(∠ BDG+∠ ABM)=90°$.
$\because ∠ N=15°$,$\therefore ∠ NMG=180°-90°-15°=75°$,
$\therefore ∠ BMN=180°-75°=105°$.
