Solution: Make an equilateral triangle ade on the same side, take AD as the side and connect BE.

So AD=AE=ED

Angle ADE= angle DAE= angle BAD+ angle BAE=60 degrees.

Because the angle is not good = angle BAC+ angle CAD

Angle BAC= 10 degree

Angle CAD=20 degrees

So the angle BAD=30 degrees

So the angle BAE=30 degrees

So BAE= BAE = 30 degrees.

Because AB=AB

So the triangle is congruent triangles ABD (SAS).

So BE=BD

Because angle BAD+ angle ABD+ angle ADB= 180 degrees.

Angle ABD=50 degrees

So the angle ADB= 100 degrees.

Because angle ADB= angle ADE+ angle BDE= 100 degrees.

So the angle BDE=40 degrees

Because the angle ACD=20 degrees

So angle CAD= angle ACD=20 degrees.

So AD=CD

So ED=CD

Because angle CAD+ angle ACD+ angle ADC= 180 degrees.

So the angle ADC= 140 degrees.

Because angle ADC= angle ADB+ angle BDC= 140 degrees.

So the angle BDC=40 degrees

So angle BDE= angle BDC=40 degrees.

Because BD=BD

So triangle BDE congruent triangles BDC (SAS)

So BE=BC

So BD=BC

So angle BDC= angle BCD=40 degrees.

Because angle BDC+ angle BCD+ angle DBC= 180 degrees.

So DBC angle = 100 degrees.