∵AB=AC且∠A=100°
∴∠ACB=∠ABC=40°
∵BD是∠ABC的平分线
∴∠DBE=20°
∵BD=BE
∴∠DBE=∠DEB=(180°-20°)÷2=80°
∴∠DEC=180°-∠DEB=180°-80°=100°