In δuvw, m∠u = (2x-17)^{\circ}(2x−17)

∘

, m∠v = (7x+16)^{\circ}(7x+16)

∘

, and m∠w = (4x-1)^{\circ}(4x−1)

∘

. find m∠u.

m∠U=11°

Step-by-step explanation:

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

In this problem

m∠U+m∠V+m∠W=180°

substitute the given values

solve for x

Combine like terns left side

Adds 2 both sides

divide by 13 both sides

Find the measure of angle U

m∠U = (2x-17)°

substitute the value of x

m∠U = (2(14)-17)=11°

∠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.

1 3 5

step-by-step explanation:

i took the test: )