Angles and Angle Measures
What You’ll Learn
Section titled “What You’ll Learn”In this lesson you’ll learn what an angle is, how to name and classify angles, and how to measure them using degrees.
The Concept
Section titled “The Concept”An angle is formed when two rays share a common endpoint (called the vertex).
- The two rays are the sides of the angle.
- The common endpoint is the vertex.
Naming angles:
- Use three points: vertex in the middle (∠ABC)
- Or just the vertex letter if clear (∠B)
- Or a number inside the angle (∠1)
Angle measurement is in degrees (°). A full circle is 360°.
Types of angles:
- Acute angle: less than 90°
- Right angle: exactly 90° (square corner)
- Obtuse angle: greater than 90° but less than 180°
- Straight angle: exactly 180° (forms a straight line)
Worked Example
Section titled “Worked Example”-
Name the angle formed by rays BA and BC with vertex B.
∠ABC or ∠B
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Classify an angle measuring 35°.
Acute angle (less than 90°)
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Classify an angle measuring 125°.
Obtuse angle (greater than 90° but less than 180°)
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If two rays form a straight line, what is the angle measure?
180° (straight angle)
Real-World Application
Section titled “Real-World Application”Angles are everywhere in daily life:
- The corner of a room or table is usually a right angle (90°).
- A door opening creates an angle that changes as it swings.
- Roof pitch, wheelchair ramps, and stair slopes are described with angles.
- When you look at a map or GPS, turns are described as angles (turn 45° left).
- In construction or DIY projects, you constantly measure and cut at specific angles.
Understanding angles helps with building, designing, navigation, and even sports (angle of a kick or throw).