Angles

An angle marks off a section of a circle by extending two rays from the center of the circle.

• The center of the circle is the vertex of the angle, the two rays are the legs of the angle.
• If the two rays form a straight line, they divide the circle in half and the angle is 180°.
• If the two rays mark off a quarter of a circle, the angle is 90° and is called a "right" angle.
• Angles are also measured in radians (no unit) where 1 ≈ 57° and 180° = π ≈ 3.14 .

• Click and drag the point С to change the angle <ABC .

• An angle of 90° is a fourth of a circle.
  • An angle of 90° is called a right angle.
  • An angle of 90° is marked by a square (make an angle of 90° in the interactivity below!).
• An angle of 180° is a half of a circle.
  • An angle of 180° is the line segment \overline{CA} where the point B is the midpoint.
• An angle of 360° is the whole circle.
  • An angle of 360° is the line segment \overline{BA} and the points А and С overlap.
  • An angle of 360° cannot be draw in the interactivity (it automatically reverts to the coterminal angle 0°).

• In the coordinate system, angles are measured counterclockwise starting from the positive x-axis.