(3x+20)°+(5x−16)°=180° solve for x

x = 22

Step-by-step explanation:

(3x + 20) + (5x - 16) = 180

remove parentheses: (a) = a

3x + 20 + 5x - 16 = 180

group like terms

3x + 5x + 20 - 16 = 180

add similar elements: 3x + 5x = 8x

8x + 20 - 16 = 180

add/subtract the numbers: 20 - 16 = 4

8x + 4 = 180

subtract 4 from both sides

8x + 4 - 4 = 180 - 4

simplify

8x = 176

divide both sides by 8

8x/8 = 176/8

simplify

x = 22

∠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.

sine

step-by-step explanation: