1. find the value of x
2. using complete sentences, describe your

x = 40

Step-by-step explanation:

The sum of the 3 angles in a triangle = 180°

Consider the triangle on the left and calculate the third angle

Subtract the sum of the 2 angles from 180

third angle = 180° - (75 + 50)° = 180° - 125° = 55°

Consider the triangle on the right

The third angle = 55° ( vertical angles )

Subtract the sum of the 2 angles from 180

x = 180 - (55 + 85) = 180 - 140 = 40

∠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.

the answer is c.

step-by-step explanation: