1. The problem is to find the labeled angles $a^\circ, b^\circ, c^\circ, d^\circ, e^\circ, f^\circ, g^\circ, h^\circ, i^\circ, j^\circ, k^\circ, m^\circ$ in triangles given side lengths and match them to the provided answers. 2. We use the Law of Sines formula: $$\frac{\sin A}{a} = \frac{\sin B}{b} = \frac{\sin C}{c}$$ where $A,B,C$ are angles opposite sides $a,b,c$ respectively. 3. For each triangle, identify the known sides and the angle to find. Use the Law of Sines to solve for the unknown angle. 4. Example for angle $a$ with sides 10 and 5 opposite $a$ and known angle respectively: $$\sin a = \frac{5}{10} \sin(\text{known angle})$$ Calculate $a$ by taking $\arcsin$. 5. Repeat this process for each labeled angle using the given side lengths and known angles. 6. Match the calculated angles to the closest values from the provided list: - $a = 44.4^\circ$ - $b = 48.6^\circ$ - $c = 53.1^\circ$ - $d = 53.1^\circ$ - $f = 15.9^\circ$ - $i = 66.4^\circ$ - $m = 36.1^\circ$ 7. The other angles $e, g, h, j, k$ can be found similarly but are not requested in the answer key. This completes the matching of labeled angles to their values using the Law of Sines and given side lengths.