Angles Around a Point

Angles Around a Point

Definition

• Angles around a point are a set of angles that share a common vertex (endpoint) and have a common initial ray (starting point).

Properties

• The sum of the measures of the angles around a point is always 360°.
• The angles around a point can be divided into two or more angles by drawing rays from the common vertex.

Types of Angles Around a Point

• Adjacent Angles: Angles that share a common vertex, a common side, and a common initial ray.
• Vertical Angles: Angles that are formed by two intersecting lines and share a common vertex.

Theorems

• The Angle Sum Theorem: The sum of the measures of the angles around a point is always 360°.
• The Vertical Angle Theorem: Vertical angles are equal in measure.

Applications

• Angles around a point are used in various fields, such as:
  • Geometry: to calculate the sum of angles in a polygon.
  • Trigonometry: to solve triangular problems.
  • Real-world applications: to calculate angles in architecture, engineering, and design.

Angles Around a Point

• Angles around a point share a common vertex and initial ray.

Properties

• The sum of measures of angles around a point is always 360°.
• Angles around a point can be divided into two or more angles by drawing rays from the common vertex.

Types of Angles Around a Point

• Adjacent Angles: Share a common vertex, side, and initial ray.
• Vertical Angles: Formed by two intersecting lines, sharing a common vertex, and are equal in measure.

Theorems

• The Angle Sum Theorem: The sum of measures of angles around a point is always 360°.
• The Vertical Angle Theorem: Vertical angles are equal in measure.

Applications

• Geometry: Calculate sum of angles in a polygon.
• Trigonometry: Solve triangular problems.
• Real-world applications: Calculate angles in architecture, engineering, and design.