The angle between the bisector of this angle and the additional ray to one of its sides is 134. Find this angle.

Let ∠ABC be given, the segment BK is the bisector of this angle, BD is the ray complementary to the side BC, then ∠DBK = 134 °.
1. Since BD is a ray complementary to the BC side, ∠DBK and ∠CBK together form a straight line (unfolded angle), which means that these angles are adjacent. In this way:
∠DBK + ∠CBK = 180 °;
134 ° + ∠CBK = 180 °;
∠CBK = 180 ° – 134 °;
∠CBK = 46 °.
2. Since BK is the bisector of ∠ABC, then ∠ABK = ∠CBK = 46 °.
In this way:
∠ABC = ∠ABK + ∠CBK;
∠ABC = 46 ° + 46 °;
∠ABC = 92 °.
Answer: ∠ABC = 92 °.