Angle Greater Than 90 Degrees

Obtuse Angle

In geometry, an obtuse bending is defined as an angle that is greater than ninety° and less than 180°. Frequently during a day in a 24 hours duration, we can run into a clock framing many obtuse angle degrees betwixt a minute hand and an hour paw. Let usa learn more about the obtuse angle and its properties.

1.	What is an Birdbrained Angle?
2.	Obtuse Angle Caste
three.	Obtuse Angle in Real Life
iv.	Obtuse Angle Triangle
five.	Astute and Obtuse Angles
vi.	FAQs on Obtuse Angle

What is an Birdbrained Bending?

The definition of an birdbrained angle in geometry states that 'an bending whose mensurate is greater than ninety° and less than 180° is chosen an obtuse bending'. In other words, an obtuse angle is an bending between a correct bending and a straight bending. Await at some of the examples of obtuse angles given beneath.

obtuse angles

Obtuse Angle Degree

In the above section, nosotros read that an bending that measures less than 180 degrees and more than ninety degrees bending is called an obtuse angle. The examples of obtuse angle degrees are 165°, 135°, 110°, 179°, 91°, etc. Hence, the obtuse angle degree lies within the ranges from xc° to 180°.

Birdbrained Angles in Real Life

We know that angles measuring greater than ninety° and less than 180° are called birdbrained angles. Here are some real-life examples of obtuse angles. Can you observe the obtuse angles in all these images? Tin can you think of more than objects in real life that include obtuse angles?

obtuse angles in real life

Some other examples of birdbrained angles in real-life are given beneath:

The angle between the hour and minute hand of a clock at 4 o'clock.
The angle betwixt the base of operations of an open laptop and its screen.
Angles formed by the blades of a ceiling fan.

Obtuse Bending Triangle

When one of the vertex angles of a triangle is greater than 90°, information technology is called an birdbrained angle triangle. An obtuse triangle can either be an isosceles or a scalene triangle. An equilateral triangle cannot exist birdbrained. The side opposite 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 angle at the same time as per the bending sum holding of a triangle. Thus, we can conclude that if one of the angles of a triangle is birdbrained, then the other two angles of a triangle must be acute angles.

obtuse angle triangle

The triangles above accept one bending greater than 90°. Hence, they are called obtuse-angled triangles or just birdbrained triangles. In an obtuse angle triangle, the sum of the squares of the two sides is less than the square of the longest side. In ΔABC, the sides measure a,b,c such that c is the largest side, nosotros have: a² + b^two < cⁱⁱ. Conversely, if in a triangle, if a² + b² < c², then the triangle is an obtuse triangle.

Acute and Obtuse Angles

At that place are dissimilar types of angles based on the measurement. Angles that measure less than xc degrees are known as acute angles, while the angles greater than ninety° merely less than 180° are known every bit birdbrained angles. Expect at the epitome of acute and obtuse angles given below followed by their difference.

acute and obtuse angles

Now, let u.s. understand acute vs obtuse bending through the table below:

Acute Bending	Birdbrained Angle
It measures less than 90 degrees.	Information technology measures greater than 90 and less than 180 degrees.
A triangle with three acute angles is known equally an astute angle triangle.	A triangle with ane obtuse angle and 2 astute angles is termed an obtuse angle triangle.
Examples of astute angles: 56°, 12°, 79°, 43°, etc.	Examples of obtuse angles: 124°, 179°, 150°, 95°, etc.

Important Notes

All angles measuring more than than ninety° and less than 180° are called obtuse angles.
In an obtuse bending triangle, the sum of the squares of the two sides is less than the foursquare of the longest side.

Thinking Out Of the Box!

Tin can a triangle take more than one obtuse angle?
Which polygon has all its internal angles as birdbrained angles?
Can there be a parallelogram without an birdbrained angle? If so, what shape tin it be?

Topics Related to Obtuse Angles

Check out a few more than interesting articles related to the obtuse angle and its properties.

Birdbrained Scalene Triangle
Isosceles Obtuse Triangle
Triangle Calculator
Acute Correct and Obtuse Angles Worksheets

Birdbrained Angle Examples

Example 1: Place the birdbrained angles from the post-obit figures.

Solution:

Option (b) - 117° and option (c) - 121° are more 90° and less than 180°. Therefore, they are obtuse angles. Therefore, 117° and 121° are obtuse angles.
Example 2: At what times, in the clocks shown below, an obtuse angle is formed?

Solution:

We can notice that in all instances, an obtuse bending is formed between the hr's hand and the minutes' manus of the clock.
- At 5:00, the hour paw is at five and the minute hand is at 12. And then, by observation, we can conclude that the angle formed is greater than 90º but less than 180°, which is an obtuse angle. Using a protractor, we can ostend that information technology is making an angle between (xc° to 180°).
- At 8:00, the 60 minutes mitt is at 8 and the infinitesimal hand is at 12. So, by observation, we can conclude that the angle formed is greater than 90º but less than 180°. Thus it is an obtuse angle.
- At 10:fifteen, the hour hand is at 10 and the minute paw is at 3. So, by ascertainment, we tin conclude that the angle formed is an obtuse angle.
- At 2:40, the hr manus is slightly to a higher place 3 and the minute hand is at viii. So, past observation, nosotros can conclude that the angle formed is greater than 90º just less than 180º. Using a protractor, nosotros tin confirm that it is making an obtuse angle.
Therefore, an obtuse angle is formed at 5:00, viii:00, 10:15, and two:forty.
Example iii: Tin an obtuse bending triangle take sides measuring 4 units, 5 units, and eight units?

Solution:

In an birdbrained triangle, the sum of the square of two sides should be less than the square of the greatest side i.eastward a² + b² < c² where c is the largest side. Allow a = iv units, b = 5 units, c = eight units (largest side) ⇒ a² = sixteen, b² = 25, c² = 64 ⇒ a² + bⁱⁱ= 16 + 25 = 41. Since 41 < 64. This implies a² + b² is less than c². Hence, the given measures grade an birdbrained bending triangle. Therefore, the sides measuring 4 units, 5 units and 8 units class an obtuse triangle.

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Practice Questions on Birdbrained Angle

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FAQs on Birdbrained Angle

What is an Obtuse Angle in Geometry?

In geometry, nosotros read about various types of angles. Each type of angle has its ain characteristics with the help of which we tin can identify information technology. Similarly, an obtuse bending is an angle that is always less than 180 degrees and is greater than xc degrees.

What does an Birdbrained Angle Await Like?

The angles measuring greater than xc° and less than 180° are called obtuse angles in geometry. The obtuse bending lies between 90° and 180° and looks like a reclined chair, an angle below the staircase, or an angle formed between a minute and an hour mitt of a clock at x:15 AM.

How do you Describe an Birdbrained Angle?

The definition of an obtuse angle in geometry states that an angle larger than 90° but less than 180° is called an birdbrained angle. We can use a protractor and marking whatsoever angle between 90° and 180° to make an birdbrained angle.

What are Some Examples of Birdbrained Angles?

145°, 150°, 178°, 149°, 91° are all examples of obtuse angle degrees equally they are more than 90° and less than 180°.

What are the Properties of Obtuse Angles?

Given below are the properties of an obtuse angle:

Angles that mensurate between 90 and 180 degrees.
Angles lie between a correct and a straight angle.

Can Two Obtuse Angles be Supplementary?

Two obtuse angles, each measuring greater than ninety° cannot course a supplementary pair of angles as the sum will be greater than 180° which doesn't satisfy the status of supplementary angles.

What is Birdbrained Angle Triangle?

A triangle with 1 obtuse bending and the other 2 acute angles is an birdbrained-angled triangle. The sum of all three interior angles will be 180 degrees.

What is Acute and Obtuse Angle?

An acute angle is the i that measures less than 90 degrees and the angles greater than xc° but less than 180° are obtuse angles.

How many Degrees is an Obtuse Angle?

The degree of an obtuse angle always lies between 90° to 180°.