Angle

Angle

Vertical Angles

Adjacentangles

Complement angle

Angle obtuse acute straight

Angle is a fundamental concept in both geometry and various branches of mathematics, with applications extending into numerous other fields such as physics, engineering, and architecture. An angle is formed by the intersection of two rays (or line segments) that share a common endpoint, known as the vertex. The amount of rotation required to superimpose one of the rays onto the other is a measure of the size of the angle.

Definition

In Euclidean geometry, an angle is typically measured in degrees, where a full circle is 360 degrees, or in radians, where a full circle is \(2\pi\) radians. The size of an angle is independent of the lengths of the rays forming it, focusing solely on the amount of rotation around the vertex.

Types of Angles

Angles can be classified based on their measure:

• A Zero angle is an angle with a measure of 0 degrees.
• An Acute angle is greater than 0 degrees but less than 90 degrees.
• A Right angle is exactly 90 degrees.
• An Obtuse angle is greater than 90 degrees but less than 180 degrees.
• A Straight angle is exactly 180 degrees.
• A Reflex angle is greater than 180 degrees but less than 360 degrees.
• A Full angle or Complete angle is exactly 360 degrees.

Angle Bisector

An angle bisector is a ray that divides an angle into two angles of equal measure. It has applications in various geometric constructions and proofs.

Measuring Angles

Angles can be measured using a variety of tools, including a protractor or by calculating the ratio of the length of the arc that the angle intercepts to the radius of the circle in radians. In more advanced mathematics, angles are also measured in gradians, where a full circle is 400 gradians.

Angles in Trigonometry

In trigonometry, angles are the basis for defining the trigonometric functions: sine, cosine, and tangent, which are fundamental in the study of right triangles and have applications in wave analysis, periodic functions, and in the circular motion of objects.

Angles in Daily Life

Angles are not just an abstract mathematical concept but have practical applications in daily life. They are used in the design and construction of buildings, in navigation, in the creation of art, and in the analysis of movements in sports.

See Also

• Complementary angles
• Supplementary angles
• Vertical angles
• Exterior angle theorem