Let's look at what happens when two lines intersect.

In this diagram, 2 straight lines, AB and CD, intersect at E

As you can see, when this occurs, 4 angles are created.
Angles x and y are opposite one another. 
The name given to a pair of angles such as these
is vertical angles.

If we were to measure each of these angles, we would find
the measure of both angle x and y to be the same.
Therefore we will state that when 2 lines intersect,
the vertical angles formed are equal in measure.

Let's look at the diagram again and see how this works....

Let's assume that the measure of angle y is 42⁰

If  angle "x"  is represented by the expression "a + 16",
can we solve for "a"?
Sure we can, remember.....
vertical angles are equal...
So, if angle x = a + 16, and angle y = 42, we can set
up the following equation:
a + 16 = 42
This is a simple one-step equation,
a + 16 = 42
    -16 = -16
     a = 26

Let's toughen it up a bit.....

This time let's not only solve for "x", but let's
figure out the measure of the angles as well.
Solution:
We can clearly see from the diagram that the angles
represented by "9x - 7" and "7x + 9" are
vertical angles.
We also know that vertical angles are equal.
Therefore we can set up the following equation:
9x - 7 = 7x + 9
9x = 7x + 16
(add 7 to both sides)
2x = 16
(subtract 7x from both sides)
x = 8
(divide both sides by 2)
Now that we know the value of "x",
we can substitute that value into our original expressions.
Let x = 8
9x - 7
9(8) - 7
72 -7 =
65⁰
7x + 9
7(8) + 9
56 + 9 =
65⁰
65⁰ = 65⁰
 

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