When two lines intersect each other, they create four angles:
In this case, the angles opposite one another are called vertical angles. As you can see, vertical angles are by definition always equal to each other. Therefore, in this case, 1 = 2, and 3 = 4. Another way to say this is that both "little angles" will equal each other and both "big angles" will equal each other. Also, note that a "little angle" plus a "big angle" will always equal 180°.
Parallel Lines
Two lines that never intersect and never get closer or farther away from one another are called parallel lines. || is the symbol for parallel lines. In the figure to the right, A || B, or line A is parallel to line B.
When two parallel lines are cut by a third line, they form a system of Vertical Angles.
In this figure, we can see that 1 =4 and 5 =8. But, because they are formed by two parallel lines, they are all equal to each other, so: 2 = 3 = 6 = 7.
There are many terms to describe these angles, such as “alternate interior” or “alternate exterior,” but these terms are not used on the test. For the GMAT, it is simply enough to know that all the little angles will always be equal to each other and all the big angles will always be equal to each other.
Additionally, you should realize that any little angle added to any big angle will always equal 180°.
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