Hi Travis. I think there's a typo somewhere in your post, but maybe we can still make some progress.

Fill in the missing information in this Algebraic proof.

Two lines intersect. Angle 1 equals ( 3x + 20) . Angle 2 = (5x - 16) , Angles 1 and 3 are vertical angles.

The measure of angle 1 = the measure of angle 3. (Vertical Angles are Congruent)

I'm pretty sure what's meant here is that "Angle 3 = (5x -16)" because otherwise the relationship between the angles isn't clear. Let me assume that something got munged and go with that.

This problem may be easier if you draw a picture. Draw one line however you want. Draw the second line so that it crosses the first. Since the angles are vertical ("diagonal" from one another -- you have to cross both lines to get from one to the other), choose two such angles on your picture and label them. If this is confusing, choose any angle as number one and go clockwise 1,2,3 and 4. Angles 1 and 3 are vertical.

So... They tell you that angle 1 and angle 3 have the same measure. They write out the equation given in the last line I quoted above. That's where you start:

Angle 1 = Angle 3

To get to the second step:

a.) _____ = (5x - 16) (Substitution)

they tell you they used substitution. What did they substitute? Notice that Angle 3 got replaced with (5x - 16) because you were given Angle 3 = (5x - 16). What do you think Angle 1 gets replaced by? Look carefully at the given information. What do you know about Angle 1?

To get to the third step:

b.) -2x + 20 = _____ (Subtraction Prop. Of Equality)

you have to subtract something

**from both sides.** Take a look at your "a" step. What is on the left hand side? What do you have to subtract from that to get "-2x + 20"? Subtract the same thing from "5x - 16" to get the term on the right for b.

To get to the fourth step:

c.) -2x = _____ (Subtraction Prop. Of Equality)

you have to subtract something different from both sides. What's different between "b" and "c" is the "20." If you subtract 20 from the left of "b", you'll get the left of "c." Because you have to do the same thing on the right, subtract 20 from your answer for the right side of "b" to get your answer to "c."

Finally, to get to the fifth step:

d.) x = _____ (Division Prop. Of Equality

you're going to divide both sides by the same thing. How do you get from "-2x" to "x"? Well, what if you divide by "-2"? Do the same thing to the right side of step four to get your final answer.

SPOILER:

As a check, I got "x = 18" for the final answer.