Obtusage angle is among the forms of angles that develop on the plane surface. In Geomeattempt, an obtuse angle is an angle that is greater than 90° and less than 180°. Often in the time of a day in a 24 hrs duration, we have the right to check out a clock framing many obtuse angle degrees in between a minute hand and also an hour hand. Let us learn more about the obtuse angle and also it's properties.

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1.What Is an Obtusage Angle?
2.Obtusage Angle Degree
3.Instances of Obtuse Angles
4.Obtuse Angle of a Triangle
5. Obtusage Angles of a Rhombus
6.Obtuse Angles of a Parallelogram
7.FAQs on Obtuse Angle

What Is an Obtusage Angle?


The definition of an obtuse angle in Geometry says that an angle whose measure is higher than 90° and much less than 180° is called an obtuse angle. In various other words, an obtusage angle is an angle between a ideal angle and a right angle.

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Obtusage Angle Degree


In the above section, we read that an angle that procedures much less than 180 degrees and more than 90 levels angle. The examples of obtuse angle levels are 165°,135°,110°,189°, 91°. Hence, the obtuse angle level lies within the ranges from 90° to less than 180°.


Examples of Obtuse Angles


We recognize that angles measuring better than 90° and also less than 180° are referred to as obtusage angles. Because of this, angles that measure 145°,150°,178°,149°, 91° are considered as obtuse angle examples. Here are some real-life examples of obtusage angles. Can you observe the obtuse angles in all these images? Can you think of more objects in real life that incorporate obtuse angles?

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Obtusage Angle of a Triangle


When one of the vertex angles of a triangle is higher than 90°, it is called an obtuse triangle. An obtusage triangle can either be an isosceles or a scalene triangle. An equilateral triangle cannot be obtuse. The side oppowebsite to the obtusage angle in the triangle is the longest side of that triangle. Similarly, a triangle can never before be a appropriate angle and also an obtuse angle at the very same time as per the angle sum residential or commercial property of a triangle. Therefore, we can conclude that if among the angles of a triangle is obtuse, then the various other 2 angles of a triangle should be acute angles.

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The triangles above have one angle greater than 90°. Hence, they are dubbed obtuse-angled triangles or ssuggest obtusage triangles. In an obtusage triangle, the amount of the squares of the 2 sides is less than the square of the longest side. In ΔABC, the sides meacertain a,b,c such that c is the largest side, thus: a2 + b2 2. Conversely, if in a triangle, if a2 + b2 2, then the triangle is an obtuse triangle.


Obtuse Angles of a Rhombus


A rhombus is a unique type of quadrilateral which includes:

four equal sidestwo pairs of parallel sidesequal opposite angles

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The sum of the interior angles of any quadrilateral is 360°. In a rhombus, consecutive angles are supplementary and also opposite angles are equal. Hence, at any kind of offered time, a rhombus has actually 2 obtuse angles that are equal and also the other two angles are acute and also they are additionally equal.


Obtuse Angles of a Parallelogram


A Parallelogram is a special type of quadrilateral which includes:

2 pairs of parallel sidesopposite sides of equal lengthsequal opposite angles

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The sum of the internal angles of any type of quadrilateral is 360°. In a parallelogram, consecutive angles are supplementary and also oppowebsite angles are equal. Thus, at any kind of offered time, a parallelogram has actually two obtusage angles that are equal and the other two angles are acute and they are likewise equal.

Important Notes

All angles measuring even more than 90° and also much less than 180° are referred to as obtuse angles.In an obtusage triangle, the amount of the squares of the 2 sides is less than the square of the longest side.

Thinking Out Of the Box!

Can a triangle have actually even more than one obtusage angle?Which polygon has all its internal angles as obtuse angles?Can there be a parallelogram without an obtusage angle? If so, what form deserve to it be?

Topics Related to Obtusage Angles

Check out few even more amazing posts regarded the obtusage angle and also its properties.


Obtuse Angle Examples


Example 1: Identify the obtusage angles from the following figures.

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Solution:

Option (b) and choice (c) are more than 90° and also less than 180°. Thus, they are obtuse angles. Option (b) and alternative (c) are obtuse angles.


Example 2: At what times, in the clocks shown listed below, an obtusage angle is formed?

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Solution:

We can observe that in all instances, an obtusage angle is formed between the hour's hand also and also the minutes' hand also of the clock.

At 5:00, the hour hand also is at 5 and the minute hand is at 12. So, by observation, we deserve to conclude that the angle formed is higher than 90º yet much less than 180º, which is an obtusage angle. Using a protractor, we deserve to confirm that it is making an angle in between (90º to 180º), hence it is an obtusage angle.At 8:00, the hour hand is at 8 and the minute hand also is at 12. So, by monitoring, we deserve to conclude that the angle formed is better than 90º but less than 180º, which is an obtuse angle. Using a protractor, we can confirm that it is making an angle in between (90º to 180º), hence it is an obtuse angle.At 10:15, the hour hand also is at 10 and the minute hand is at 3. So, by observation, we deserve to conclude that the angle developed is better than 90º however much less than 180º, which is an obtuse angle. Using a protractor, we have the right to confirm that it is making an angle between (90º to 180º), therefore it is an obtuse angle.At 2:40, the hour hand also is slightly over and also the minute hand is at 8. So, by observation, we deserve to conclude that the angle created better than 90º but much less than 180º, which is an obtusage angle. Using a protractor, we deserve to confirm that it is making an angle in between (90º to 180º), for this reason it is an obtusage angle.

As such, an obtuse angle is developed at 5:00, 8:00, 10:15, and 2:40.

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Example 3: Can an obtusage angle triangle have actually sides measuring 4 systems, 5 systems, and 8 units?

Solution:

In an obtusage triangle, the sum of the square of 2 sides must be less than the square of the best side i.e a2 + b2 2 where c is the largest side. Let a = 4 systems, b = 5 units, c = 8 systems (biggest side) ⇒ a2 = 16, b2 = 25, c2 = 64 ⇒ a2 + b2 = 16 + 25 = 41. Because 41 2 + b2 is much less than c2. Hence, the given procedures develop an obtuse angle triangle. Because of this, the sides measuring 4 systems, 5units and 8 devices form an obtusage triangle.