In ΔLMN, the measure of ∠N=90°, MN = 8.6 feet, and NL = 6.4 feet. Find the measure of ∠M to the nearest degree.

37°

Step-by-step explanation:

Find the detailed diagram of the triangle in the attachment below.

Using the SOH, CAH TOA trigonometry ratio to get the angle M.

NL will be the opposite since it's facing the angle M that we are looking for, and side MN will be the adjacent side.

Using TOA;

tan ∠M= opposite/adjacent

tan∠M = NL/MN

tan∠M = 6.4/8.6

tan∠M= 0.7442

∠M= arctan 0.7442

∠M = 36.66°

∠M = 37° (to the nearest degree)

Step-by-step explanation:

The value of angle M can be found with the help of trigonometric functions. Since is a right-angle triangle and both known sides are legs, the tangent function is used:

x+14

step-by-step explanation:

∠1≅∠2 by the alternate exterior angles theorem.

step-by-step explanation:

given, a ∥ b and ∠1 ≅ ∠3 .we have to prove that e ∥ f

we know that ∠1≅∠3 and that a || b because they are given. we see that by the alternate exterior angles theorem. therefore, ∠2≅∠3 by the transitive property. so, we can conclude that e || f by the converse alternate exterior angles theorem.

we have to fill the missing statement.

transitivity property states that if a = b and b = c, then a = c.

now, given ∠1≅∠3 and by transitivity property ∠2≅∠3 .

hence, to apply transitivity property one angle must be common which is not in result after applying this property which is ∠1.

the only options in which ∠1 is present are ∠1 and ∠2, ∠1 and ∠4

∠1 and ∠4 is not possible ∵ after applying transitivity we didn't get ∠4.

hence, the missing statement is ∠1≅∠2.

so, ∠1≅∠2 by the alternate exterior angles theorem.