# Angles

In geometry, an angle is formed by two rays or line segments that share a common endpoint, known as the vertex. Angles are measured in degrees and are fundamental to understanding geometric shapes, relationships, and transformations.

Key Concepts:

Vertex: The common endpoint of the two rays or line segments forming the angle.

Arms: The two rays or line segments that form the angle. These extend from the vertex.

Degree Measure: Angles are measured in degrees, with a full circle being 360 degrees.

### Types of Angles

Right Angle: An angle that measures exactly 90 degrees.

Straight Angle: An angle that measures exactly 180 degrees, forming a straight line.

Acute Angle: An angle that measures less than 90 degrees.

Obtuse Angle: An angle that measures more than 90 degrees but less than 180 degrees.

Reflex Angle: An angle that measures more than 180 degrees but less than 360 degrees.

Complimentary Angles: Complementary angles are two angles whose measures add up to 90 degrees. If one angle is known, the other can be found by subtracting the known angle from 90 degrees. For example, if one angle is 30 degrees, its complement is 60 degrees (since 30° + 60° = 90°).

Supplementary Angles: Supplementary angles are two angles whose measures add up to 180 degrees. If one angle is known, the other can be found by subtracting the known angle from 180 degrees. For example, if one angle is 110 degrees, its supplement is 70 degrees (since 110° + 70° = 180°).

Conjugate Angles: Conjugate angles are often used in the context of complex numbers or wave theory rather than in basic geometry. In complex numbers, the conjugate of a complex angle involves the complex conjugate of the associated number, changing the sign of the imaginary part. In a broader geometric sense, it could also refer to angles related through some form of inversion or reflection, but this is more advanced and less commonly encountered in basic geometry.

### Types of Angles Drawings:

These examples and drawings illustrate various types of angles, their measurements, and relationships. Understanding angles is essential for solving geometric problems, describing shapes, and analyzing spatial configurations.