Table of Contents
Angles
Angle Definition: Angles are formed when two lines intersect. The angle is the space between the two lines. The angle has two arms, or sides. An angle also has a vertex, or the point where the two lines intersect. The angle has a measure, which is the size of the angle. The measure is measured in degrees.
Positive Angles
A positive angle is an angle that is greater than zero degrees and less than 180 degrees. Positive angles are often used in geometry to measure the size of a turn or rotation. When a line is turned or rotated around a point, the angle between the original line and the rotated line is a positive angle.
Negative Angles
A negative angle is an angle that is measured in the opposite direction as a positive angle. A negative angle is measured using the same unit of measure as a positive angle. For example, if a positive angle is measured in degrees, then a negative angle is measured in degrees as well.
Properties of Angles
Important properties of the angle are:
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For one side of a straight line, the sum of all the angles always measures 180 degrees.
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The sum of all angles always measures 360 degrees around a point.
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An angle is a figure where, from a common position, two rays appear. The vertex of the angle is called this point and its arms or sides are called the two rays forming the angle.
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A reflex angle is called an angle which is greater than 180 degrees but less than 360 degrees.
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They form a linear pair of angles if two opposite angles add up to 180 degrees.
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The two opposite pairs of angles formed are called vertically opposed angles where two lines parallel each other.
Types of Angles
There are six types of angles commonly known in geometry:
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Acute Angles: When the measurement of an angle is between 0 to 90 degrees.
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Obtuse Angles: The opposite of an acute angle is an obtuse angle. It is the angle that lies between 90 degrees and 180 degrees; the obtuse angle is greater than 90 degrees and less than 180 degrees.
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Right Angles: A right angle is equal to 90 degrees. Any angle of fewer than 90 degrees is an acute angle, and an obtuse angle is an angle greater than 90 degrees.
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Straight Angles: A straight angle is 180 degrees when measured.
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Reflex Angles: A reflex angle is any angle that has a measure that is greater than 180 degrees but less than 360 degrees (coinciding with 0 degrees).
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Full Rotation: Complete rotation, or full angle, is considered an angle equal to 360 degrees. When one of the arms takes a full rotation to form an angle, it is made.
Angle Types Based on Rotation
Angles can be of 2 types based on the direction of rotation:
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Positive Angles
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Negative Angles
Positive Angles
They are the angles determined from the base in the counterclockwise direction. Positive angles are often used to show geometry angles. From the origin, if an angle is drawn in the (+x, +y) plane, it forms a positive angle.
Negative Angles
Negative angles are the angles determined from the base in a clockwise direction. From the origin, if an angle is drawn towards the (x, -y) plane, it forms a negative angle.
Pair of Angles
By combining two angles, we can create different types of angles, such as:
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Complementary angles: If the sum of the two angles is 180°, they are called complementary angles.
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Supplementary angles: If the sum of the two angles is 90°, they are called supplementary angles.
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Linear Pair: If the non-common arms of adjacent angles are exactly opposite each other or extend in the other direction, then they are called linear pairs. By linear, it is clear that they form a straight line.
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Adjacent angles: If two angles are attached to a common arm and have a common vertex, so they are considered adjacent angles, and the non-common arms are on either side of the common arm, too.
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Vertically Opposite Angles: The angle created on either side of the common vertex is called vertical angles or vertically opposite angles if both lines converge at a single point (called the vertex).
