Sv is an angle bisector of ∠rst. if m∠rsv = (2x + 8)° and m∠rst = (6x − 26)°, find x.

x = 21

Step-by-step explanation:

Given that SV is the angle bisector of ∠RST, then

∠RSV = ∠TSV, thus

∠RSV + ∠TSV = ∠RST ← substitute values

2x + 8 + 2x + 8 = 6x - 26, that is

4x + 16 = 6x - 26 ( subtract 6x from both sides )

- 2x + 16 = - 26 ( subtract 16 from both sides )

- 2x = - 42 ( divide both sides by - 2 )

x = 21

∠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.