Hurry 20points
what is the measure of angle e?
m∠e = °
what is the length of ef rounded to the nearest hundredth?
ef ≈

m<E=55

Hope this helps!

Measure of angle E is 55°

Length of the side EF is 12.49 units

Step-by-step explanation:

We are given the triangle EDF with angle measures ∠D = 43° and ∠F = 82°.

As, we know, The sum of the measures of angles in a triangle is 180°.

So, we have,

∠E + ∠D + ∠F = 180°

i.e. ∠E + 43° + 82° = 180°

i.e. ∠E = 180° - 125°

i.e. ∠E = 55°

Thus, the measure of angle E is 55°.

Further we have,

i.e.

i.e.

i.e.

i.e. EF = 12.49 units

Thus, the length of the side EF is 12.49 units.

answer: there are x+184 pages in olivia's book.

step-by-step explanation:

let the total number of pages in the book which olive has already read be x.

then if olive has 184 pages left to read, then the total number of pages are in olive's book= pages she has read+pages she has left to read

therefore, the total number of pages in olivia's book=

hence, there are x+184 pages in olivia's book.

∠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.