Measure of ∠M to the nearest degree is [tex]65^{0}[/tex].
The law of cosine states that the square of any one side of a triangle is equal to the difference between the sum of squares of the other two sides and double the product of other sides and cosine angle included between them.
Given
k = 76 inches
l = 30 inches
m = 69 inches
From the law of cosines
Cos <M = [tex]\frac{k^{2} +l^{2} -m^{2} }{2.k.l}[/tex]
Cos <M = [tex]\frac{76^{2} +30^{2} -69^{2} }{2.76.30}[/tex]
Cos <M = [tex]\frac{1915}{4560}[/tex]
Cos <M = 0.42
<M = [tex]cos^{-1} (0.42)[/tex]
<M ≈ [tex]65^{0}[/tex]
Hence, measure of ∠M to the nearest degree is [tex]65^{0}[/tex].
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