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Basic Trigonometric Angles

When two lines, segments, or rays touch or cross one another, they form an angle or angles. In the case of two intersecting lines, the result is four different angles. When two segments intersect, they can form one, two, or four angles; the same goes for two rays.

These examples are just some of the ways that you can form angles. Geometry, for example, describes an angle as being created when two rays have a common endpoint. In practical terms, you can form an angle in many ways, from many figures. The business with the two rays means that you can extend the two sides of an angle out farther to help with measurements, calculations, and practical problems.

Describing the parts of an angle is pretty standard. The place where the lines, segments, or rays cross is called the vertex of the angle. From the vertex, two sides extend.

Naming angles by size

You can name or categorize angles based on their size or measurement in degrees:

  • Acute: An angle with a positive measure less than 90 degrees

  • Obtuse: An angle measuring more than 90 degrees but less than 180 degrees

  • Right: An angle measuring exactly 90 degrees

  • Straight: An angle measuring exactly 180 degrees (a straight line)

  • Oblique: An angle measuring more than 180 degrees


Naming angles by letters

How do you name an angle? Why does it even need a name? In most cases, you want to be able to distinguish a particular angle from all the others in a picture. When you look at a photo in a newspaper, you want to know the names of the different people and be able to point them out. With angles, you should feel the same way.

You can name an angle in one of three different ways:

  • By its vertex alone: Often, you name an angle by its vertex alone because such a label is efficient, neat, and easy to read. Here, you can call the angle A.

  • By a point on one side, followed by the vertex, and then a point on the other side: For example, you can call the angle here angle BAC or angle CAB. This naming method is helpful if someone may be confused as to which angle you're referring to in a picture.

    Make sure you always name the vertex in the middle.

  • By a letter or number written inside the angle: Usually, that letter is Greek; here, however, the angle has the letter w. Often, you use a number for simplicity if you're not into Greek letters or if you're going to compare different angles later.

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