Given: triangles abc and dbc are isosceles, m∠bdc = 30°, and m∠abd = 155°. find m∠abc, m∠bac, and m∠dbc.

Since the triangle DBC is isosceles, angles ∠BCD and ∠CDB are equal.
∠CDB=30° ⇒ ∠BCD=30°. The sum of all angles in the triangle is 180°.
∠DBC=180°-30°-30°=120°.
∠ABC=155°-120°=35°. Triangle ABC is also isosceles, so two angles that lie on the base are equal, too
∠BAC=∠ABC=35°