What Is an Obtuse Angle Definition Properties and Solved Examples
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 Meaning and Degree Measure
1. What is an obtuse angle?
An obtuse angle is an angle that measures more than 90° but less than 180°. It is wider than a right angle and smaller than a straight angle. For example, angles measuring 100°, 120°, and 150° are all obtuse angles.
2. How do you identify an obtuse angle?
You can identify an obtuse angle by checking if its measure is greater than 90° and less than 180°.
- Step 1: Measure the angle using a protractor.
- Step 2: Compare the measurement with 90° and 180°.
- If it lies between them, it is an obtuse angle.
3. What is the difference between acute, right, and obtuse angles?
The main difference is based on their degree measure.
- Acute angle: less than 90°
- Right angle: exactly 90°
- Obtuse angle: more than 90° but less than 180°
4. Can a triangle have an obtuse angle?
Yes, a triangle can have exactly one obtuse angle. A triangle with one angle greater than 90° is called an obtuse triangle. Since the sum of angles in a triangle is 180°, only one angle can be obtuse.
5. What is an example of an obtuse angle?
An angle measuring 120° is a common example of an obtuse angle. Since 120° is greater than 90° and less than 180°, it satisfies the definition of an obtuse angle.
6. How do you draw an obtuse angle?
To draw an obtuse angle, measure an angle between 90° and 180° using a protractor.
- Step 1: Draw a baseline ray.
- Step 2: Place the protractor at the vertex.
- Step 3: Mark a point greater than 90° (for example, 130°).
- Step 4: Draw the second ray through the marked point.
7. Is 180 degrees an obtuse angle?
No, 180° is not an obtuse angle; it is a straight angle. An obtuse angle must be strictly less than 180°, so 180° does not qualify.
8. What shapes have obtuse angles?
Many geometric shapes can have obtuse angles, depending on their structure.
- Obtuse triangles (one angle > 90°)
- Obtuse-angled quadrilaterals like some parallelograms
- Irregular polygons with angles between 90° and 180°
9. What is the complement of an obtuse angle?
An obtuse angle does not have a complement because complementary angles must add up to 90°. Since an obtuse angle is already greater than 90°, it cannot form a complementary pair.
10. What is the supplement of an obtuse angle?
The supplement of an obtuse angle is an acute angle that adds up to 180° with it. For example:
- If the obtuse angle is 120°
- Supplement = 180° − 120° = 60°
