Understanding Angles | Classification, Measures, and Properties in Mathematics

Angle

In mathematics, an angle is a geometric figure formed by two rays or line segments sharing a common endpoint, called the vertex

In mathematics, an angle is a geometric figure formed by two rays or line segments sharing a common endpoint, called the vertex. The rays or line segments that form the angle are known as the sides of the angle. An angle is usually measured in degrees (°) or radians (rad).

The size or magnitude of an angle determines its measure. Angles can be classified based on their measures into different categories:

1. Acute Angle: An acute angle is an angle whose measure is greater than 0 degrees, but less than 90 degrees.
Example: A ∠ABC measuring 40 degrees is an acute angle.

2. Right Angle: A right angle is an angle whose measure is exactly 90 degrees.
Example: A ∠XYZ measuring 90 degrees is a right angle.

3. Obtuse Angle: An obtuse angle is an angle whose measure is greater than 90 degrees but less than 180 degrees.
Example: A ∠PQR measuring 150 degrees is an obtuse angle.

4. Straight Angle: A straight angle is an angle whose measure is exactly 180 degrees. It forms a straight line.
Example: The line opposite to a right angle, forming a straight line, is a straight angle.

5. Reflex Angle: A reflex angle is an angle whose measure is greater than 180 degrees but less than 360 degrees.
Example: A ∠DEF measuring 270 degrees is a reflex angle.

Angles can also be classified based on their position relative to other angles:

1. Vertical Angles: Vertical angles are a pair of opposite angles created by the intersection of two lines. They have equal measures.
Example: If two lines intersect and form four angles, the vertically opposite angles have the same measure.

2. Adjacent Angles: Adjacent angles are two angles that share a common side and a common vertex but have no common interior points.
Example: In the figure below, ∠ABC and ∠CBD are adjacent angles.

3. Complementary Angles: Complementary angles are two angles that add up to 90 degrees. Each angle is called the complement of the other.
Example: If ∠PQR = 30 degrees, then its complement ∠QRS would measure 60 degrees.

4. Supplementary Angles: Supplementary angles are two angles that add up to 180 degrees. Each angle is called the supplement of the other.
Example: If ∠LMN = 100 degrees, then its supplement ∠MNO would measure 80 degrees.

Understanding angles and their properties is crucial for various mathematical applications, such as geometry, trigonometry, and physics.

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