Obtuse Angle

Learning about obtuse angles is important in geometry as it forms the basis for properties of various 2D-shapes including triangles, parallelograms, trapezoids, etc. An obtuse angle is commonly found in geometry and real-life too. From shapes to real-life objects such as clock hands or pizza slices, obtuse angle examples are found everywhere. In this article, we will explore the meaning, measurement, formulas, and applications of obtuse angles, especially within an obtuse angle triangle.

Table Of Contents

• What is an Obtuse Angle?
• Degree of Obtuse Angle
• Obtuse Angle Triangle
• Properties of Obtuse-Angle Triangle
• Obtuse Angles in Real-Life
• Difference between Obtuse and Acute Angle
• Practice Questions
• Conclusion
• FAQs on Obtuse Angle

 

What is an Obtuse Angle?

The obtuse angle definition states that any angle measuring more than 90° and less 180° is considered an obtuse angle. It is greater than an acute angle and right angle but is less than a straight line. In geometry, obtuse angles are formed when two lines meet each other at a point and measure of degree between them is more than 90° but less than 180°. These lines are called the arms of an obtuse angle and the point where they meet is known as the vertex. 

 

Degree of Obtuse Angle 

The obtuse angle degree range is from 90° to 180°. Any angle that is less than 180 degrees but greater than 90 degrees is called an obtuse angle. It is greater than a right angle and acute angle but less than 180°. For example, ∠130°, ∠145°, and ∠175° are all obtuse angles.

In geometry, obtuse angles often appear in triangles, parallelograms, and trapezoids, making them essential in understanding 2D shapes. Below are some common obtuse angles:

• ∠105°

• ∠133°

• ∠145°

• ∠167°

• ∠150°

All of these fall under the obtuse angle category because they are greater than a right angle (90°<) and smaller than a straight line (<180°).

Obtuse Angle Triangle

An obtuse angle triangle is a triangle that has one obtuse angle that is the measure of one of its angles greater than 90° but less than 180°. There are some important properties of an obtuse triangle that make it an important shape in geometry, architecture and construction.

Properties of an Obtuse-Angle Triangle

• Has one obtuse angle (> 90°).

• The other two angles are always acute.

• Can be Scalene or Isosceles, but never Equilateral.

 

Example of Obtuse Angle Triangle:

A triangle with angles 120°, 30°, and 30° is an Obtuse Angle Triangle.

A real-life example of an Obtuse Angle Triangle is the wide angle formed when a book is opened.

Obtuse Angles in Real-Life

You can find acute angles all around you:

• Pizza slice corners

• Arrows on road signs

• The hands of a clock at 4:00

• Scissors when widely open

These examples show that understanding obtuse angles is not just academic - it’s useful in everyday life.

 

Difference Between Obtuse, Acute & Right Angle

Let's learn about different features of types of angles:

This comparison helps us clearly distinguish between obtuse and acute angles.

Practice Questions

1. Is 145° an acute angle?

2. Classify 170°, 90°, and 110° as acute, right, or obtuse.

3. What is the range of obtuse angle degrees?

4. In triangle ABC, if ∠A = 80°, ∠B = 10°, find ∠C. Is it obtuse?

5. Can a triangle have two acute angles and one right angle?

Conclusion

The obtuse angle is an essential geometric concept, appearing in triangles, polygons, and real-world shapes. With a measurement always less than 180° and greater than 90°, obtuse angles help define many mathematical relationships and shape properties. Whether it’s an obtuse angle triangle or identifying angles, mastering this concept builds a solid foundation in geometry. Learn more about how angles form the foundation of geometry with easy explanations and real-life applications at Orchids International School.

FAQs on Obtuse Angle

1. Explain obtuse angle.

Answer: An obtuse angle is an angle that is greater than 90 degrees but less than 180 degrees. It looks wider than a right angle.

2. What is the difference between an obtuse angle and an acute angle?

Answer: An acute angle is less than 90 degrees, while an obtuse angle is more than 90 degrees. Acute angles are sharp and small, but obtuse angles are wide and open.

3. Can a triangle have more than one obtuse angle?

Answer: No! A triangle can only have one obtuse angle, because the total of all three angles in a triangle must be 180 degrees. The triangle that has one obtuse angle is called an obtuse triangle.

4. How do you identify an obtuse angle?

Answer:  To identify an obtuse angle, check if the angle is bigger than a right angle (90°) but not as flat as a straight line (180°). You can use a protractor to measure and confirm.

5. What are some real-life examples of obtuse angles?

Answer: Some examples of obtuse angles in real life include:

1. The hands of a clock at 10:10

2. The open lid of a box

3. The arms of a person stretching wide

4. Certain road signs or roof designs

6. What tool is used to measure an obtuse angle?

Answer: A protractor is used to measure angles, including obtuse angles. Place the center of the protractor at the vertex and read the outer scale to measure angles over 90 degrees.

7. Is 120 degrees an obtuse angle?

Answer: Yes, 120 degrees is an obtuse angle because it is more than 90 degrees but less than 180 degrees.

8. What is the range of an obtuse angle?

Answer: An obtuse angle is always greater than 90° and less than 180°. So, its range is:

90° < obtuse angle < 180°