Understanding Angles | A Comprehensive Guide to Types, Measurements, and Applications in Mathematics

Angle

In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex

In mathematics, an angle is a geometric figure formed by two rays or line segments that share a common endpoint, known as the vertex. The rays or line segments are often referred to as the sides of the angle.

Angles are typically measured in degrees (°) or radians (rad). In the degree system, a complete revolution or a full angle is equal to 360 degrees. Each degree is further divided into 60 minutes (‘) and each minute is divided into 60 seconds (“). So, for example, an angle of 45 degrees can also be written as 45° or 45 degrees, 0 minutes, and 0 seconds.

Angles can be classified based on their size or position. Some common classifications include:

1. Acute Angle: An angle that is less than 90 degrees is called an acute angle. It is often depicted as a small angle.

2. Right Angle: An angle that measures exactly 90 degrees is called a right angle. It is often depicted as a square measure (∟).

3. Obtuse Angle: An angle that measures between 90 and 180 degrees is called an obtuse angle. It is larger than a right angle and often depicted as a wide angle.

4. Straight Angle: An angle that measures exactly 180 degrees is called a straight angle. It is a straight line formed by two opposite rays or segments.

5. Reflex Angle: An angle that measures between 180 and 360 degrees is called a reflex angle. It is larger than a straight angle but smaller than a full revolution.

6. Complementary Angles: Two angles are said to be complementary if their sum is exactly 90 degrees. For example, angles measuring 30 and 60 degrees are complementary.

7. Supplementary Angles: Two angles are said to be supplementary if their sum is exactly 180 degrees. For example, angles measuring 60 and 120 degrees are supplementary.

Angles are used in various mathematical concepts and applications, such as trigonometry, geometry, physics, and engineering. They help measure and describe the rotation, direction, and position of objects or shapes in space.

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