How to Identify an Obtuse Angle in Geometry?
The concept of obtuse angle plays a key role in mathematics and is widely applicable to both real-life situations and exam scenarios. Understanding obtuse angles helps students classify shapes, solve geometry problems, and notice patterns in everyday objects.
What Is Obtuse Angle?
An obtuse angle is an angle that measures more than 90° but less than 180°. This means the angle opens wider than a right angle. You’ll find this concept applied in geometry, measurement of triangles, and daily-life shape observation. Obtuse angles are common in polygons, clocks, and even in some tools found at home!
Key Facts: Types of Angles Table
| Angle Type | Degree Range | Example |
|---|---|---|
| Acute | 0° < angle < 90° | 45° in a triangle |
| Right | Exactly 90° | Corner of book |
| Obtuse | 90° < angle < 180° | 120° in clock hands |
| Straight | Exactly 180° | Straight line |
| Reflex | 180° < angle < 360° | 200° corner in art |
Obtuse Angle Examples
- The hands of a clock at 4 o'clock form a 120° obtuse angle.
- A boomerang often has an angle of about 130°.
- The open lid of a laptop when tilted back forms an obtuse angle.
- Traffic signboards in “Yield” shapes (triangles) include obtuse corners.
- Inside a regular pentagon, each angle is 108° and is obtuse.
Difference: Acute, Right & Obtuse Angles
| Angle Type | Degree Range | How It Looks |
|---|---|---|
| Acute | < 90° | Sharp, small angle |
| Right | 90° | “L”-shaped corner |
| Obtuse | > 90° but < 180° | Wide, open angle |
Obtuse Angles in Triangles & Shapes
A triangle with one angle more than 90° is called an obtuse angled triangle. Only one obtuse angle is possible in a triangle, and the other two angles must be acute. Many real-life shapes (like pentagons, parallelograms, and even irregular polygons) contain obtuse angles. When classifying triangles or polygons, always check angle measurements to spot obtuse ones.
| Shape | Obtuse Angles? | Example |
|---|---|---|
| Obtuse Triangle | Yes (1 only) | Triangle with angles 30°, 40°, 110° |
| Rectangle | No | All angles are 90° |
| Regular Pentagon | Yes | All angles are 108° |
How to Draw an Obtuse Angle (Geometry Tools)
Drawing an obtuse angle is simple with a protractor:
1. Draw a straight line using a ruler.2. Place the center of the protractor at one end of the line.
3. Mark a point at your desired obtuse angle (for example, 120°).
4. Remove the protractor and join this point to the starting point using a straight edge.
5. You have made a perfect obtuse angle!
Obtuse Angle Word Problem (Solved)
Question: In triangle ABC, angle A = 40° and angle B = 120°. What is angle C? Is ABC an obtuse angled triangle?
1. The sum of all angles in a triangle is 180°.2. Add angles A and B: 40° + 120° = 160°.
3. Subtract from 180° to find angle C: 180° - 160° = 20°.
4. Triangle ABC has one angle > 90° (angle B), so it is an obtuse angled triangle.
Obtuse Angle in Real Life
- Scissors when open widely form an obtuse angle.
- Ramp or hill roads have obtuse turns for slow vehicles.
- Regular pentagon tables (furniture design) have obtuse corners.
- The position of the hour and minute hands at 10:05 on a clock creates an obtuse angle.
Quick Classroom Tip
A quick way to remember obtuse angles: they “open wide” and are bigger than a right angle (90°) but not as flat as a straight angle! If the corner looks “too far open,” it’s likely obtuse. Vedantu’s teachers recommend using your fingers or a corner of a paper for quick comparison during practice.
Related Concepts and Internal Links
Obtuse angle knowledge helps you compare with other types of angles, understand triangle classification by angles, and connect with the basic angle definition and measurements. For deeper learning, explore right angle triangle theorem and types of triangles for more geometry practice.
Try These Yourself
- Draw a triangle with one obtuse angle and two acute angles. Label the degrees.
- Name five examples of obtuse angles you see at home or school.
- Spot the obtuse angle: 92°, 89°, 135°, 75°, 180°.
- Is a 170° angle obtuse or straight?
Frequent Errors and Misunderstandings
- Thinking 180° is obtuse (it’s a straight angle, not obtuse).
- Confusing obtuse with reflex angles (reflex angles are greater than 180°).
- Assuming triangles can have two obtuse angles (they can have only one).
We explored obtuse angle—from definition, differences, examples, drawing, and common mistakes, to connecting with triangles and real objects. Practice recognizing obtuse angles visually and with tools. Continue learning with Vedantu for easy explanations, step-by-step tips, and guided online classes in maths!
FAQs on Obtuse Angle – Definition, Degree & Examples
1. What is an obtuse angle in maths?
An obtuse angle is an angle that measures greater than 90° but less than 180°. It's wider than a right angle (90°) but narrower than a straight angle (180°).
2. How many degrees are there in an obtuse angle?
An obtuse angle measures between 90° and 180°. Any angle within this range is classified as obtuse.
3. Give 3 examples of obtuse angles from daily life.
Examples of obtuse angles in everyday life include:
- The angle formed by the hands of a clock at 2 o'clock.
- The corner of an open book.
- Many angles in architectural structures like church steeples or bridges.
4. Which triangle has an obtuse angle?
An obtuse-angled triangle is a triangle that contains one obtuse angle (an angle greater than 90°). The other two angles in an obtuse triangle must be acute (less than 90°).
5. How do I identify an obtuse angle in a shape?
To identify an obtuse angle, use a protractor to measure the angle or visually compare it to a right angle (90°). If the angle is clearly wider than 90° but less than 180°, it's obtuse.
6. Can a triangle have more than one obtuse angle?
No, a triangle cannot have more than one obtuse angle. The sum of angles in any triangle is always 180°. If two angles were obtuse, their sum alone would exceed 180°.
7. Why is a 180° angle not considered obtuse?
A 180° angle is a straight angle, not an obtuse angle. Obtuse angles are defined as being *greater than* 90° but *less than* 180°.
8. Are reflex angles obtuse?
No, reflex angles are angles greater than 180° and less than 360°. Obtuse angles are between 90° and 180°.
9. How is an obtuse angle used in architecture?
Obtuse angles are frequently used in architecture to create visually appealing and structurally sound designs. Many arches, roof structures, and decorative elements incorporate obtuse angles.
10. Do all quadrilaterals have obtuse angles?
No, not all quadrilaterals have obtuse angles. Rectangles and squares, for example, have only right angles (90°). However, many quadrilaterals, such as parallelograms or irregular quadrilaterals, can contain one or more obtuse angles.
11. What is the difference between an obtuse and an acute angle?
An acute angle measures less than 90°, while an obtuse angle measures between 90° and 180°. Acute angles are smaller than right angles, while obtuse angles are larger than right angles.
12. How do you construct an obtuse angle using a protractor and compass?
1. Draw a line segment. 2. Place the protractor's center on one endpoint of the segment. 3. Mark a point at the desired obtuse angle measurement (e.g., 120°). 4. Draw a line segment from the endpoint through the marked point. 5. You can optionally use a compass to check the accuracy of the angle measurement by drawing arcs.
