1. **Problem Statement:** Identify the figure in which angles $B_1$ and $B_2$ are complementary. 2. **Definition:** Complementary angles are two angles whose measures add up to $90^\circ$. 3. **Analysis of Figures:** - Figure A: Angles $B_1$ and $B_2$ are adjacent but no indication they sum to $90^\circ$. - Figure B: Angles $B_1$ and $B_2$ share vertex $B$ but no clear right angle. - Figure C: Angles $B_1$ and $B_2$ are perpendicular, one vertical and one horizontal, forming a right angle. - Figure D: Angles $1$ and $2$ are formed by intersecting lines but no clear complementary relationship. 4. **Conclusion:** Figure C shows $B_1$ and $B_2$ as complementary angles because they form a right angle ($90^\circ$). **Final answer:** Figure C