Find the missing values of the variables. The diagram is not to scale.
119
106°
74

x = 93, y = 74

Step-by-step explanation:

y and 106 are supplementary angles, in other words,

y+106 = 180

y = 74

All the angles in a quadrilateral added up is equal to 360 degrees, so

x+74+74+119 = 360

x = 93

∠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.

x-150=475   x=625

step-by-step explanation:

if the bike after the sale ($150) is $475 then just simply add 150 to 475.