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Angle - Geometric Characteristics Of Angles

measurement lines revolution congruent

An angle is typically classified into four categories including acute, right, obtuse, and straight. An acute angle is one which has a degree measurement greater than 0° but less than 90°. A right angle has a 90° angle measurement. An obtuse angle has a measurement greater than 90° but less than 180°, and a straight angle, which looks like a straight line, has a 180° angle measurement.

Two angles are known as congruent angles if they have the same measurement. If their sum is 90°, then they are said to be complementary angles. If their sum is 180°, they are supplementary angles. Angles can be bisected (divided in half) or trisected (divided in thirds) by rays protruding from the vertex.

When two lines intersect, they form four angles. The angles directly across from each other are known as vertical angles and are congruent. The neighboring angles are called adjacent because they share a common side. If the lines intersect such that each angle measures 90°, the lines are then considered perpendicular or orthogonal.

In addition to size, angles also have trigonometric values associated with them such as sine, cosine, and tangent. These values relate the size of an angle to a given length of its sides. These values are particularly important in areas such as navigation, astronomy, and architecture.

See also Geometry.

Perry Romanowski

KEY TERMS

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Congruent angles

—Angles which have the same measurement.

Degree

—A unit of measurement used to describe the amount of revolution of an angle denoted by the symbol °. There are 360° in a complete revolution.

Initial side

—The ray of an angle which falls on the x-axis when an angle is in its standard position.

Radian

—A unit of angle measurement that relates the amount of revolution of an angle in terms of a the radius of a circle. There are 2π radians in a complete revolution.

Terminal side

—The ray of an angle in its standard position which extends away from the x-axis.

Vertex

—The point at which the two sides of an angle meet.

Vertical angles

—Angles created by the intersection of two lines which are directly across from each other and share a common vertex.

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almost 6 years ago

Kayla, he was right because he said greater than 0 and less than 90 it doesn't say it is exactly 0 or exactly 90.

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about 6 years ago

it help me study a lot thanks for duing this page

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about 1 year ago

i don't understated i just wanted characteristics about an angle

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about 6 years ago

help me a lottttttt

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almost 9 years ago

An acute angle isn't between 0 and 90 degrees. Why is because 0 degrees would be a straight line which is 180 degrees. 90 degrees alos isn't because that would be a rigth angle.

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about 8 years ago

angle

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almost 9 years ago

Sorry for the other comment but the real acute degrees woudl be 1-89 degrees.