The main story has 150 times as many pages as the prologue there is 750 pages in all how many pages in the main story

There are approximately 745 pages in main story

Solution:

Let "x" be the number of pages in main story

Let "y" be the number of pages in prologue

Given that there are 750 pages in all

Therefore,

number of pages in main story + number of pages in prologue = 750

x + y = 750 eqn 1

The main story has 150 times as many pages as the prologue

Therefore, a equation is framed as:

number of pages in main story = 150(number of pages in prologue)

x = 150y eqn 2

Let us solve eqn 1 and eqn 2

Substitute eqn 2 in eqn 1

150y + y = 750

151y = 750

y = 4.967

Substitute y = 4.967 in eqn 2

x = 150(4.967)

x = 745.05

Thus there are approximately 745 pages in main story

a. -0.3 > -0.33

∠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.