Ronald works in an Ornithology (bird maintenance) department. Students asked him to find out the best estimate of the local bird population. So he tied a belt around the legs of 40 birds. A few days later, he observed 520 birds, 34 of which had belts. To the nearest whole number, what is the best estimate for the bird population?

618 birds.

Step-by-step explanation:

Let the estimated number of birds=x

Out of x birds, he tied a belt around the legs of 40 birds.

When he observed 520 birds, 34 of which had belts.

Expressing each as a ratio

Cross Multiply

34x=520X40

x=520X40÷34=611.7≈618

There are an estimated 618 birds.

∠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.