1: Introduction
Geometry is always a logical puzzle. The GMAT gives you a tiny piece of information about a figure, and you must logically deduce the information the question wants. Geometry questions require you to follow a series of “if…then” statements, constantly solving the puzzle, piece by piece, to the correct answer.
II. Lines and Angles (Beginner)
| The most basic element in geometry is the point: |
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| If we have two points, we can connect them to form a line: |
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| When two lines originate from the same point, they form an angle: |
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The point of intersection is the vertex and the two lines form the sides of the angle. The angle is designated in a number of ways. It is  BAC where the middle letter is the vertex, A where A is the vertex, or x where x is located inside the angle.
Angles are measured in degrees, denoted by this symbol: °. For example, a 30 degree angle would be written as 30°. When placed next to one another, angles may be added up.
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The sum of x + y here is 90°. |
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The sum of x + y here is 180°. Notice that x and y create a straight line. All straight lines are 180°. |
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A beam of light is shown in the figure to the left reflecting off a mirror. What is the value of x?
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| Solution
Because these three angles form a straight line, they must add up to 180°. Therefore:
x + 3x + x = 180°
5x = 180°
x = 36°
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