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Angles

An angle is a geometric figure consisting of two
rays with a common endpoint. It looks like
this:

Figure %: Angle ABC

The common endpoint is called the vertex of the angle; in this case the
vertex is point A, which is a part of the ray
AB as well as the ray AC. The angle can be called either angle CAB or angle
BAC. The only rule in naming an angle is that the vertex

**must** always be
the middle "initial" of the angle. The symbol for an angle is this:

Figure %: The symbol for angle ABC

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Measuring Angles

Long ago people wanted to measure angles, so numbers were arbitrarily assigned
to determine the size of angles. Under this arbitrary numbering system, one
complete rotation around a point is equal to a 360 degree rotation. (There
is another unit of measure for angles besides degrees called radians, in
which one full rotation is equal to 2*Π* radians; in this text we will use
degrees as our default unit for measuring angles.) Two angles with the same
measure are called congruent angles. Congruence in angles is symbolized by
a small arc drawn in the region between rays. Congruent angles are drawn with
the same number of such arcs between their rays. An angle's measure determines
how it is classified.

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Zero Angles

An angle with a measure of zero degrees is called a zero angle. If this is
hard to visualize, consider two rays that form some angle greater than zero
degrees, like the rays in the . Then
picture one of the rays rotating toward the other ray until they both lie in the
same line. The angle they create has been
shrunk from its original measure to zero degrees. The angle that is now formed
has a measure of zero degrees.

Figure %: A zero angle

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Right Angles

An angle with a measure of 90 degrees is called a right angle. A right
angle is symbolized with a square drawn in the
corner of the angle.

Figure %: A right angle

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Straight Angles

An angle with a measure of 180 degrees is called a straight angle. It looks
just like a line. Don't mix up straight angles with zero angles.

Figure %: A straight angle

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Acute and Obtuse angles

Another way to classify angles by their measures is to consider whether the
angle's measure is greater or less than 90 degrees. If an angle measures less
than 90 degrees, it is called an acute angle. If it measures more than 90
degrees, it is called an obtuse angle. Right angles are neither acute nor
obtuse. They're just right.