No. We have 3 angles of triangle ABC congruent to 3 corresponding angles of triangle LMN. That is AAA. To use ASA, you need two angles and an included side. With three angles, you can prove the triangles similar, but not congruent.
First I converted the equation terms into sine and cosine. and Substitution: Common Denominator Created: Multiply each term by the LCD: Substitution: Recall ⇒ Distribute and collect all terms on one side: Factor and set each factor equal to 0: ⇒ ⇒ The 2nd factor provides only possible answer 109.5 degrees