When two lines intersect four angles are formed.
In this lesson we will learn how to determine the measure
of three of those angles if we have been given
the measure of one.
Look at the diagram below:

As you can see the two intersecting lines have created 4 angles. 
The measure of one of the angles has been given as 72⁰.
The other 3 angles are labeled a, b and c.
Our task is to determine the measure of each of those
other 3 angles.
Actually, this is a very simple task.
Determining the measure of angle "b" is as easy
as remembering that the 72⁰ angle and angle "b"
are known as vertical angles, and vertical angles are equal.
That means that the measure of angle "b" is also 72⁰.
We can also see that angles "a" and "c" are also vertical angles.
So if we can determine the measure of one of the angles, the other
will have the same measure.
To do this we need to see that the original 72⁰angle and angle "a"
are supplementary angles.
Supplementary angles are two angles whose sum is180⁰.
We know they are supplementary
 because the angles combine to create a straight line.
And as you know a straight line is a straight angle,
and the measure of a straight angle is 180⁰.
Now that we have reviewed the important vocabulary
all we need to do is subtract 72 from 180,
and that will give us the measure of angle "a".
180 - 72 = 108
The measure of angle "a" is 108⁰.
And, because angle "a" and angle "c" are vertical angles,
the measure of angle "c" is also 108⁰.

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