Find the value of X in the triangle shown below

x = sqrt(32)

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2+ b^2 = c^2

7^2 + x^2 = 9^2

49+x^2 = 81

Subtract 49 from each side

x^2 = 81-49

x^2 =32

Take the square root of each side

sqrt(x^2) = sqrt(32)

x = sqrt(32)

answer: can and shows the work

step-by-step explanation:

∠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.