3. Find the mean of each group of numbers:
27, 27, 27, 27, 27
11, 17, 13, 16, 18
52, 61, 59, 63, 57
36, 48, 52, 37, 50, 46, 38, 51
79, 89, 87, 78, 88, 89
1.1, 1.3, 1.2, .4
26.1, 23.4, 28.6, 20.4, 18.0, 21.1
63.02, 48.12, 52.35, 60.03-
3, 2 ¾, 2 ¼

1. 27

2. 15

3. 58.4

4. 44.75

5. 40.725

6. 55.88

7.  2.6666666666667

∠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.