An angle is known as an obtuse angle if its measure is greater than 90 degrees but less than 180 degrees.
Understanding Obtuse Angles
To determine if an angle is obtuse, you need to know its degree measure. An obtuse angle falls within a specific range: it is wider than a right angle (90°) but not as wide as a straight angle (180°).
Think of it this way:
- Greater than a right angle: If you imagine the corner of a square or a book, that's a right angle. An obtuse angle opens up wider than that.
- Less than a straight angle: A straight line forms a straight angle. An obtuse angle is not a flat line; it still has a discernible "corner" or vertex.
How to Measure an Angle
The most common tool for measuring angles is a protractor. Here's how you can use one to identify an obtuse angle:
- Place the protractor's center: Align the small hole or mark at the base of the protractor with the vertex (the point where the two lines of the angle meet).
- Align one arm: Line up one of the angle's arms with the 0° mark on the protractor's scale. (Note: Protractors often have two scales; choose the one that starts at 0° along the aligned arm).
- Read the other arm: Follow the second arm of the angle to where it crosses the protractor's scale. The number it points to is the angle's measure in degrees.
If the number you read is anywhere between 91° and 179° (inclusive), then you have an obtuse angle.
For a visual guide on using a protractor, you can refer to resources like Math Is Fun's Protractor page.
Comparing Angle Types
Understanding other types of angles helps in clearly distinguishing an obtuse angle.
| Angle Type | Description | Degree Measure |
|---|---|---|
| Acute | An angle that is sharp and narrower. | Greater than 0° and less than 90° |
| Right | An angle that forms a perfect corner. | Exactly 90° |
| Obtuse | An angle that is wider than a right angle. | Greater than 90° and less than 180° |
| Straight | An angle that forms a straight line. | Exactly 180° |
| Reflex | An angle that measures more than a straight angle. | Greater than 180° and less than 360° |
| Full | An angle that completes a full circle. | Exactly 360° |
This table provides a quick reference for angle classification. For more detailed information on types of angles, you might find resources like Khan Academy's Angles page helpful.
Practical Examples
Obtuse angles are found everywhere in the real world:
- Door opening: When a door is opened wide, but not completely flat against the wall, it often forms an obtuse angle with the doorframe.
- Clock hands: At 4 o'clock, the angle between the hour and minute hand is obtuse.
- Roof pitch: Some architectural roof designs feature obtuse angles.
- Scissors: When scissors are opened wide to cut, the angle between the blades can be obtuse.
In summary, to know if an angle is obtuse, simply measure it. If its degree measurement falls between 90° and 180°, it's an obtuse angle.
