解:（4）如圖⑦，當(dāng)$DA = DE$時(shí)，又$AD = DC，$$BE = DE，$$\therefore\angle CAD=\angle C = 27^{\circ}。$設(shè)$\angle B = x，$則$\angle BDE = x，$$\angle BAD=\angle AED = 2x。$$\because\angle B+\angle C+\angle BAC = 180^{\circ}，$$\therefore x + 27^{\circ}+2x + 27^{\circ}=180^{\circ}，$解得$x = 42^{\circ}，$$\therefore\angle B = 42^{\circ}。$如圖⑧，當(dāng)$AD = AE$時(shí)，$\because AD = CD，$$BE = DE，$$\therefore\angle CAD=\angle C = 27^{\circ}。$設(shè)$\angle B = x，$則$\angle BDE = x，$$\angle ADE=\angle AED = 2x。$又$\angle ADB=\angle DAC+\angle C = 54^{\circ}，$$\angle ADB=\angle ADE+\angle BDE = 3x，$$\therefore 3x = 54^{\circ}，$解得$x = 18^{\circ}，$$\therefore\angle B = 18^{\circ}。$如圖⑨，當(dāng)$AE = DE$時(shí)，又$BE = DE，$$\therefore\angle ADB = 90^{\circ}。$又$AD = CD，$$\therefore\angle C=\angle CAD=\frac{1}{2}\angle ADB = 45^{\circ}\neq27^{\circ}。$故$\angle B$的度數(shù)為18°或42°。
