Solve for a. 4(a + 3)=12 + 4a

all real numbers

−3

no solution

−1

4(a + 3)=12 + 4a

=> 4a + 12 = 12 + 4a

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All real numbers

Step-by-step explanation:

4 ( a + 3 ) = 12 + 4a

First, distibute on the left:

4 ( a + 3 )

( 4 x a ) + ( 4 x 3 )

4a + 12

4a + 12 = 12 + 4a

Subtract 12 from each side:

4a = 4a

Subtract 4a from each side:

0 = 0

∠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.