How to Identify and Use Obtuse Angles in Geometry
Before we answer the question, let’s understand what an angle is. An angle is a fundamental part of geometry that has been used as an important aspect of architecture and engineering for a long time. We use them to measure changes in the path of motion of ships, stars, airplanes, etc.
But, how do they form?
Angles are formed when two rays or lines intersect at a point. There are different types of Angles in geometry. In this article, we will discuss Obtuse Angles.
Obtuse Angle: Definition
A simple definition of an obtuse angle is “an angle which is greater than 90o but less than 180o.” Or, we can also say that “it is the angle formed when a ray rotates between 90o and 180o around a point.”
During the day, we can see a clock forming many obtuse angle degrees between the minute hand and the hour hand. Let us understand more about the obtuse angles and their properties.
Obtuse Angle Pic
Obtuse angle measuring 120o.
Obtuse Angles in Real Life
Below are some real-life examples of obtuse angles.
Obtuse Angle Pictorial representation
If we look up the sofa or other objects and the highlighted angles, then we observe that the angle formed is greater than the right angle, i.e., 90o but less than the straight angle, i.e., 180o. So, these objects are examples of obtuse angles.
Properties of an Obtuse Angle
The angles always range from 90o and 180o. It means an obtuse angle is greater than 90 degrees and smaller than a straight angle that is 180 degrees.
This angle will resemble a quarter of the circle but not half of the circle.
If we divide the circle into four pieces, an obtuse angle will occupy between \[\frac{1}{4}\] and \[\frac{1}{2}\] of a circle.
In an obtuse triangle, there will always be an obtuse angle.
Conclusion
An obtuse angle is defined as 'an angle whose measure is larger than 90° but less than 180o'. A protractor can be used to measure or draw an obtuse angle. This is a helpful tool that students will learn to use in geometry lessons.
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FAQs on What Is an Obtuse Angle?
1. What is an obtuse angle in Maths?
An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees. It is larger than a right angle (which is exactly 90°) and smaller than a straight angle (which is exactly 180°). Any angle falling within this range is classified as obtuse.
2. How are obtuse angles different from acute and right angles?
The main difference lies in their measurement relative to a 90-degree angle. Here’s a simple comparison:
- Obtuse Angle: Measures greater than 90° but less than 180°.
- Right Angle: Measures exactly 90°.
- Acute Angle: Measures less than 90° but more than 0°.
3. Can you give some examples of an obtuse angle?
Certainly. Any angle with a measure such as 100°, 125°, or 160° is an obtuse angle. You can also find examples in everyday life:
- The hands of a clock when they show 5 o'clock.
- The angle of a laptop screen when it is tilted far back.
- The way a door opens wider than a corner.
- The shape of a boomerang.
4. What is an obtuse-angled triangle?
An obtuse-angled triangle, or simply an obtuse triangle, is a triangle where one of the three interior angles is an obtuse angle (greater than 90°). The other two angles in this type of triangle must be acute. The side of the triangle that is opposite the obtuse angle is always the longest side.
5. Why can a triangle have only one obtuse angle?
A triangle can only have one obtuse angle because the sum of all three interior angles in any triangle must equal exactly 180 degrees. If a triangle had two obtuse angles (for instance, 95° and 105°), their sum alone (200°) would already exceed the 180° total limit. This makes it geometrically impossible for a triangle to contain more than one obtuse angle.
6. How can you identify an obtuse angle without a protractor?
You can use a right angle as a simple reference. The corner of a standard piece of paper or a book forms a perfect 90° right angle. To check an unknown angle, place the corner of the paper at the angle's vertex. If the angle you are measuring is wider than the paper's corner, it is an obtuse angle. If it is smaller, it's an acute angle.
7. Can a square or a rectangle ever have an obtuse angle?
No, it's not possible. A core defining property of both a square and a rectangle is that all four of their interior angles are right angles (exactly 90°). If even one angle were changed to be obtuse (greater than 90°), the shape would cease to be a square or rectangle and would become a different type of quadrilateral, such as a trapezoid or an irregular polygon.
