40°
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To find the measure of angle M in triangle KLM, apply the Law of Cosines using the given side lengths to calculate the angle measure.
Use the Law of Cosines:
- cos(∠M) = (k² + l² - m²) / (2kl)
Substitute the given values:
- cos(∠M) = (6.3² + 6.1² - 4.2^2) / (2*6.3*6.1)
- cos(∠M) ≈ 0.771
- ∠M = arccos (0.771)
- ∠M ≈ 40° (using calculator)
