Given: Triangles ABC and DBC are isosceles, m∠BDC = 30°, and m∠ABD = 155°. Find m∠ABC, m∠BAC, and m∠DBC.

Answer 1

m∠DBC = (180-30)/2 = 75°
m∠ABC = m∠ABD - m∠DBC = 155-75 = 80°
so m∠A = (180 - 2*80) = 20°

Now you know all the angles.