A local garden contains 1/12 lettuce, 3/12 carrots, 4/12 of corn and the rest red radishes. How much of the garden is radishes? How much of the garden is either corn or lettuce?

The answer to your question is a) 4/12    b) 5/12

Step-by-step explanation:

Data

Lettuce = 1/12

Carrots = 3/12

Corn = 4/12

Red radishes = ?

a)

The total of the garden is 12/12

Red radishes = 12/12 - 1/12 - 3/12 - 4/12

                      = 12/12 - 8/12

                      = 4/12

4/12 of the garden are red radishes.

b)

Corn of lettuce = 1/12 + 4/12

                         = 5/12

5/12 of the garden are corn or lettuce.

∠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.