You are part of a construction company that is supposed to build houses. An architect has left plans to build houses on each island. Bridges connect the islands. Island A and Island B have a total of 20 houses. Island A and Island C have a total of 13 houses. Island B and Island C have a total of 15 houses. A total of 24 houses is to be built on the three islands. Determine how many houses are to be built on each island. Explain how you arrived at your answer in detail.

Problem:

You are part of a construction company that is supposed to build houses. An architect has left plans to build houses on each island. Bridges connect the islands. Island A and Island B have a total of 20 houses. Island A and Island C have a total of 13 houses. Island B and Island C have a total of 15 houses. A total of 24 houses is to be built on the three islands. Determine how many houses are to be built on each island. Explain how you arrived at your answer in detail.

Facts:

A and Island B have a total of 20 houses

A and Island C have a total of 13 houses

B and Island C have a total of 15

There is a total of 24 houses

Explanation:

The 3 houses will have a total of 24, but A and  B have a total of 20 houses meaning that C is 4. However from the data: A and Island C have a total of 13 houses and B and Island C have a total of 15 we know B must be more because C will always have the same value meaning B is 2 more than A. With the knowledge of C being 4 because B and A are 20, B must be 11 and A Must be 9 as 11 is 2 more than 9 but they both still equal 20.

A is 9

B is 11

C is 4

∠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.