Name, measure and classify angles

Key notes:

1. Understanding Angles

  • Definition: An angle is formed by two rays (sides) that share a common endpoint called the vertex.
  • Notation: Angles are usually named using three points (the vertex is always the middle point) or a single letter representing the vertex (e.g., ∠ABC or ∠A).

2. Measuring Angles

  • Protractor: A protractor is a tool used to measure angles in degrees (°).
  • Measurement Range: Angles can be measured from 0° to 360°.
    • Zero Angle: 0°
    • Acute Angle: Less than 90°
    • Right Angle: Exactly 90°
    • Obtuse Angle: Between 90° and 180°
    • Straight Angle: Exactly 180°
    • Reflex Angle: Between 180° and 360°

3. Classifying Angles

  • Acute Angles (0° < angle < 90°): Angles that are smaller than a right angle.
  • Right Angles (angle = 90°): Angles that form a perfect corner.
  • Obtuse Angles (90° < angle < 180°): Angles larger than a right angle but smaller than a straight angle.
  • Straight Angles (angle = 180°): Angles that are in a straight line.
  • Reflex Angles (180° < angle < 360°): Angles larger than a straight angle.

4. Angle Relationships

  • Complementary Angles: Two angles that add up to 90°.
  • Supplementary Angles: Two angles that add up to 180°.
  • Adjacent Angles: Angles that share a common vertex and side but do not overlap.
  • Vertical Angles: Angles that are opposite each other when two lines intersect; they are always equal.

Learn with an example

➡️ Is this angle acute, right, obtuse, or straight?

  • acute
  • right
  • obtuse
  • straight

Look at this angle:

This angle measures exactly 180°. This angle is a straight angle.

➡️ Look at this angle:

Name this angle: ______

In this angle, the vertex is A:

Name the angle using the points B, A, and C. The symbol ∠ means angle, so it is written first. Be sure to write the vertex in the middle:

∠BAC and ∠CAB

You can also name the angle using just the vertex:

∠A

➡️ Is this angle acute, right, obtuse, or straight?

  • acute
  • right
  • obtuse
  • straight

Look at this angle:

This angle measures more than 90° but less than 180°. This angle is an obtuse angle.

Let’s practice!🖊️