Classifying Angles

Classifying Angles

Acute Angles

• An acute angle is an angle whose measure is between 0° and 90°.

• Acute angles

  Classifying Angles

  Acute Angles

  • An acute angle is an angle whose measure is between 0° and 90°.
  • Acute angles are less than a right angle (90°).
  • Examples: 30°, 45°, 60°
  • Properties: always has a positive tangent value and a sine value between 0 and 1.

  Obtuse Angles

  • An obtuse angle is an angle whose measure is between 90° and 180°.
  • Obtuse angles are greater than a right angle (90°) but less than a straight angle (180°).
  • Examples: 100°, 120°, 150°
  • Properties: always has a negative tangent value and a sine value between 0 and 1.

  Right Angles

  • A right angle is an angle whose measure is exactly 90°.
  • Examples: 90°
  • Properties: has a tangent value of 0 and a sine value of 1.

  Straight Angles

  • A straight angle is an angle whose measure is exactly 180°.
  • Examples: 180°
  • Properties: has a tangent value of 0 and a sine value of -1.

  Reflex Angles

  • A reflex angle is an angle whose measure is between 180° and 360°.
  • Examples: 210°, 240°, 300°
  • Properties: always has a negative tangent value and a sine value between -1 and 0.

  Note: These of angles are essential in trigonometry and geometry, as they enable us to understand the relationships between different angles and their properties.

  Right Angles

  • A right angle is an angle whose measure is exactly 90°, forming a 90-degree corner.
  • Examples: 90°, the angle between two perpendicular lines, or the angle between the x and y axes in a Cartesian coordinate system.
  • Properties: has a tangent value of 0 and a sine value of 1, which means that the opposite side and adjacent side are equal in length, forming a perfect right triangle.

  Straight Angles

  • A straight angle is an angle whose measure is exactly 180°, forming a straight line.
  • Examples: 180°, the angle between two parallel lines, or the angle between the x-axis and a line parallel to the x-axis in a Cartesian coordinate system.
  • Properties: has a tangent value of 0 and a sine value of -1, which means that the opposite side is equal in length to the adjacent side, but opposite in direction.

  Reflex Angles

  • A reflex angle is an angle whose measure is between 180° and 360°, forming a "bent" line.
  • Examples: 210°, 240°, 300°, the angles formed by two non-parallel lines that intersect.
  • Properties: always has a negative tangent value and a sine value between -1 and 0, which means that the opposite side is longer than the adjacent side, but opposite in direction.

  Note: These classifications can be used to identify and analyze various types of angles, which is crucial in solving problems involving right triangles, trigonometric identities, and geometric shapes.

  can be used to solve various trigonometric problems and are essential in understanding many mathematical concepts.

  less than a right angle (90°).

• Examples: 30°, 45°, 60°

Obtuse Angles

• An obtuse angle is an angle whose measure is between 90° and 180°.
• Obtuse angles are greater than a right angle (90°) but less than a straight angle (180°).
• Examples: 100°, 120°, 150°

Reflex Angles

• A reflex angle is an angle whose measure is between 180° and 360°.
• Reflex angles are greater than a straight angle (180°) but less than a full circle (360°).
• Examples: 210°, 240°, 300°

Angle Classification

• An acute angle measures between 0° and 90°.
• Acute angles are less than a right angle.
• Examples of acute angles: 30°, 45°, 60°.

Obtuse Angles

• An obtuse angle measures between 90° and 180°.
• Obtuse angles are greater than a right angle but less than a straight angle.
• Examples of obtuse angles: 100°, 120°, 150°.

Reflex Angles

• A reflex angle measures between 180° and 360°.
• Reflex angles are greater than a straight angle but less than a full circle.
• Examples of reflex angles: 210°, 240°, 300°.