It is known that the angle ABC is 74, and the ray DB is its bisector. Calculate the DBC angle.

The condition says that the angle ABC = 74 degrees is given, where BD ∈ ∠ABC, and also BD is the bisector of the angle ABC. Find the DBC angle.
Solution.
By definition, a bisector is a ray emanating from the apex of an angle that divides the angle into two equal angles. Since, according to the condition, BD is the bisector of the angle ABC, then:
∠ DBC = 1/2 * ∠ ABC.
Substitute the values of the degree measure of the angle ABC and get:
∠ DBC = 1/2 * 74 ° = 37 °.
Answer: ∠ DBC = 37 °.