An Obtuse Angle Measures Between
Obtuse Angle
In geometry, an obtuse angle is defined every bit an bending that is greater than 90° and less than 180°. Often during a twenty-four hours in a 24 hours elapsing, we can see a clock framing many obtuse angle degrees between a minute mitt and an hr hand. Permit us acquire more than about the obtuse bending and its properties.
| 1. | What is an Obtuse Angle? |
| ii. | Obtuse Angle Degree |
| iii. | Obtuse Angle in Real Life |
| 4. | Obtuse Angle Triangle |
| v. | Acute and Obtuse Angles |
| six. | FAQs on Obtuse Bending |
What is an Obtuse Angle?
The definition of an obtuse angle in geometry states that 'an angle whose measure is greater than ninety° and less than 180° is called an obtuse bending'. In other words, an obtuse bending is an angle betwixt a right angle and a direct angle. Expect at some of the examples of obtuse angles given below.
Obtuse Bending Caste
In the above section, we read that an angle that measures less than 180 degrees and more than 90 degrees angle is called an obtuse bending. The examples of obtuse bending degrees are 165°, 135°, 110°, 179°, 91°, etc. Hence, the obtuse angle degree lies within the ranges from 90° to 180°.
Obtuse Angles in Existent Life
We know that angles measuring greater than 90° and less than 180° are called birdbrained angles. Hither are some existent-life examples of obtuse angles. Tin you discover the obtuse angles in all these images? Tin you recall of more objects in real life that include obtuse angles?
Some other examples of obtuse angles in real-life are given below:
- The angle between the hour and minute paw of a clock at 4 o'clock.
- The angle betwixt the base of an open laptop and its screen.
- Angles formed past the blades of a ceiling fan.
Obtuse Bending Triangle
When 1 of the vertex angles of a triangle is greater than 90°, it is called an obtuse angle triangle. An birdbrained triangle tin can either be an isosceles or a scalene triangle. An equilateral triangle cannot exist obtuse. The side reverse to the obtuse angle in the triangle is the longest side of that triangle. Similarly, a triangle can never be a right angle and an obtuse bending at the same time as per the bending sum property of a triangle. Thus, we can conclude that if i of the angles of a triangle is obtuse, then the other 2 angles of a triangle must be acute angles.
The triangles above have one angle greater than 90°. Hence, they are called obtuse-angled triangles or merely obtuse triangles. In an obtuse angle triangle, the sum of the squares of the two sides is less than the foursquare of the longest side. In ΔABC, the sides mensurate a,b,c such that c is the largest side, nosotros accept: a2 + b2 < cii. Conversely, if in a triangle, if a2 + b2 < c2, and so the triangle is an birdbrained triangle.
Acute and Birdbrained Angles
There are different types of angles based on the measurement. Angles that mensurate less than ninety degrees are known every bit acute angles, while the angles greater than 90° simply less than 180° are known as obtuse angles. Wait at the image of acute and birdbrained angles given below followed by their difference.
Now, let united states of america sympathise acute vs birdbrained angle through the table beneath:
| Acute Angle | Obtuse Angle |
|---|---|
| Information technology measures less than 90 degrees. | Information technology measures greater than ninety and less than 180 degrees. |
| A triangle with 3 acute angles is known every bit an astute angle triangle. | A triangle with i obtuse angle and two acute angles is termed an obtuse angle triangle. |
| Examples of acute angles: 56°, 12°, 79°, 43°, etc. | Examples of obtuse angles: 124°, 179°, 150°, 95°, etc. |
Of import Notes
- All angles measuring more 90° and less than 180° are called obtuse angles.
- In an obtuse angle triangle, the sum of the squares of the two sides is less than the square of the longest side.
Thinking Out Of the Box!
- Can a triangle have more 1 obtuse angle?
- Which polygon has all its internal angles equally birdbrained angles?
- Tin there be a parallelogram without an obtuse bending? If and so, what shape tin it exist?
Topics Related to Birdbrained Angles
Check out a few more interesting articles related to the birdbrained angle and its properties.
- Obtuse Scalene Triangle
- Isosceles Birdbrained Triangle
- Triangle Calculator
- Astute Right and Obtuse Angles Worksheets
Obtuse Bending Examples
-
Case 1: Identify the obtuse angles from the following figures.
Solution:
Option (b) - 117° and choice (c) - 121° are more than 90° and less than 180°. Therefore, they are obtuse angles. Therefore, 117° and 121° are birdbrained angles.
-
Example 2: At what times, in the clocks shown below, an obtuse angle is formed?
Solution:
We can observe that in all instances, an obtuse angle is formed between the hour's hand and the minutes' manus of the clock.
- At 5:00, the hour mitt is at 5 and the minute hand is at 12. So, by observation, nosotros tin can conclude that the angle formed is greater than 90º but less than 180°, which is an birdbrained angle. Using a protractor, we tin can ostend that it is making an angle betwixt (90° to 180°).
- At 8:00, the hr hand is at viii and the minute hand is at 12. So, by ascertainment, nosotros can conclude that the bending formed is greater than 90º but less than 180°. Thus information technology is an obtuse angle.
- At 10:15, the 60 minutes hand is at 10 and the minute hand is at 3. So, by ascertainment, we can conclude that the angle formed is an obtuse angle.
- At 2:40, the 60 minutes mitt is slightly to a higher place 3 and the infinitesimal hand is at 8. So, past observation, nosotros can conclude that the bending formed is greater than 90º merely less than 180º. Using a protractor, we tin can confirm that it is making an obtuse angle.
Therefore, an obtuse angle is formed at 5:00, viii:00, 10:15, and 2:40.
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Exercise Questions on Birdbrained Angle
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FAQs on Obtuse Bending
What is an Obtuse Bending in Geometry?
In geometry, nosotros read nigh various types of angles. Each blazon of angle has its own characteristics with the aid of which we tin can identify it. Similarly, an obtuse angle is an bending that is e'er less than 180 degrees and is greater than xc degrees.
What does an Obtuse Angle Look Like?
The angles measuring greater than xc° and less than 180° are chosen obtuse angles in geometry. The obtuse angle lies between xc° and 180° and looks similar a reclined chair, an angle below the staircase, or an angle formed between a minute and an 60 minutes paw of a clock at x:xv AM.
How exercise you Draw an Obtuse Angle?
The definition of an obtuse angle in geometry states that an angle larger than xc° but less than 180° is called an obtuse angle. Nosotros can use a protractor and mark any angle between 90° and 180° to brand an obtuse angle.
What are Some Examples of Obtuse Angles?
145°, 150°, 178°, 149°, 91° are all examples of obtuse angle degrees as they are more than 90° and less than 180°.
What are the Properties of Obtuse Angles?
Given below are the backdrop of an obtuse angle:
- Angles that measure betwixt 90 and 180 degrees.
- Angles lie between a right and a straight angle.
Tin Two Birdbrained Angles be Supplementary?
Two obtuse angles, each measuring greater than 90° cannot form a supplementary pair of angles as the sum will be greater than 180° which doesn't satisfy the condition of supplementary angles.
What is Obtuse Angle Triangle?
A triangle with 1 obtuse angle and the other two astute angles is an obtuse-angled triangle. The sum of all three interior angles volition be 180 degrees.
What is Acute and Obtuse Angle?
An acute angle is the one that measures less than 90 degrees and the angles greater than ninety° but less than 180° are obtuse angles.
How many Degrees is an Obtuse Angle?
The degree of an obtuse angle always lies between xc° to 180°.
An Obtuse Angle Measures Between,
Source: https://www.cuemath.com/geometry/obtuse-angle/
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