In triangle LMN, LM=6, MN=9, and LN=7. Find m angle m to the nearest tenth of a degree

To solve for the measure of angle m, use the cosine law formula.

c^2 = a^2 + b^2 - 2ab cos (C)

in the given situation

(LN) ^2 = (LM) ^2 + (MN) ^2 - 2 (LM) (MN) cos (m)

substitute the given values

7^2 = 6^2 + 9^2 - 2 (6) (9) cos (m)

-68 = 2 (6) (9) cos (m)

cos (m) = - 0.6296

m = arcos (-0.6296)

m = 129.0 degrees