Naming and Classifying Angles
Two rays sharing an endpoint create an angle. Learn how to name them correctly and classify them by their measure.
Introduction
Angles are everywhere — every corner of a room, every slice of pizza, every tick of a clock. Naming them precisely and classifying their size is foundational for everything that follows in geometry.
Past Knowledge
Rays and endpoints (1.1.2).
Today's Goal
Name angles using three-letter notation and classify them as acute, right, obtuse, or straight.
Future Success
Angle Addition (1.3.2), angle relationships (1.3.3-1.3.4), and every proof involving angles.
Key Concepts
What Is an Angle?
An angle is formed by two rays (the sides) that share a common endpoint (the vertex).
Naming Angles
- Three letters: or — the vertex letter () is always in the middle.
- By vertex alone: — only if there is no ambiguity (only one angle at that vertex).
- By number: — when an angle is labelled with a number in a diagram.
Classifying by Measure
| Type | Measure |
|---|---|
| Acute | |
| Right | |
| Obtuse | |
| Straight |
Worked Examples
Naming an Angle
Two rays and share endpoint . Name the angle.
The vertex is , which goes in the middle.
Answer: (or ).
Classifying an Angle
Classify if .
, so the angle is between a right and a straight angle.
Answer: Obtuse.
Common Pitfalls
Vertex Not in the Middle
In three-letter notation, the vertex is always the middle letter. has vertex , not or .
Real-Life Applications
Clock Angles
At 3:00 the hour and minute hands form a 90° right angle. At 6:00 they form a 180° straight angle. Calculating the exact angle at any time combines rate-of-change thinking with angle classification.
Practice Quiz
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