Riverside Elementary School is holding a school-wide election to choose a school color. 5/8 of the votes were for blue, 5/9 of the remaining votes were for green 48 votes were for red. How many votes were for blue? how many votes were for green? if every student got one vote, but there were 25 students absent on the day of the vote, how many students are there at Riverside Elementary School

288 votes

Step-by-step explanation:

wright out what you know

Blue: 5/8

Green: 5/9 (of 3/8 because it is the remaining parts) so 5/24

Red: 1 - (5/8 + 5/24) = 1/6

Find the total amount of people

You know that 1/6 of the population is 48, so the total population is 288 (48×6)

Multiply the total population by the fractions to get the number of votes

∠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.

45

step-by-step explanation: