Help with Angle Pair Theorems????

[help;-;]

What's the m of angle ABC

 

[lev888]

What's the m of angle ABC

What are the theorems? What's the relationship between the marked angles?

 

[pka]

Surely you can solve \(3x-2=2x+46~??\)

 

[civic00sdz]

What's the m of angle ABC

Do you still need help with this problem?

 

[Steven G]

Do you still need help with this problem?

Go ahead and solve it so others can learn from it.

 

[civic00sdz]

Sounds good Jomo.

So here we have two parallel lines AB and DE (while they can be segments I mean to refer to them as lines)

And then we have line CE acting as a transverse line

This means that some special angles will form

In our case we will look at the angels knows as corresponding angles

Corresponding angles are equal and in this case that means:

angle ABC and angle DEB are equal to each other

So that means we can set 2x + 46 equal to 3x - 2

In equation form it looks like this:

2x + 46 = 3x - 2

Now we just do the algebra:

2x + 46 = 3x - 2 ( start with this equation and solve for x )

2x +48 = 3x ( here we added 2 to both sides )

48 = x ( here we subtracted 2x from both sides )

So we know that x = 48

We are not done yet though

The question asks for the measure of angle ABC

The measure of angle ABC = 2x + 46 but we already know what x is because we solved for it

So lets plug in x = 48, into this equation:

The measure of angle ABC = 2x + 46

The measure of angle ABC = 2(48) + 46

The measure of angle ABC = 96 + 46

The measure of angle ABC = 142

And that is our final answer.