Obtuse angle is one of the types of angle that kind on the aircraft surface. In Geometry, an obtuse edge is one angle the is higher than 90° and also less 보다 180°. Often during a day in a 24 hours duration, we have the right to see a clock framing numerous obtuse angle degrees between a minute hand and also an hour hand. Let united state learn much more about the obtuse angle and it's properties.

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1.What Is an Obtuse Angle?
2.Obtuse angle Degree
3.Examples that Obtuse Angles
4.Obtuse edge of a Triangle
5. Obtuse angles of a Rhombus
6.Obtuse angles of a Parallelogram
7.FAQs top top Obtuse Angle

What Is an Obtuse Angle?


The definition of an obtuse angle in Geometry claims that an edge whose measure is greater than 90° and also less 보다 180° is called an obtuse angle. In various other words, an obtuse edge is an angle between a appropriate angle and also a directly angle.

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Obtuse angle Degree


In the over section, we read that one angle the measures much less than 180 levels and an ext than 90 degrees angle. The instances of obtuse angle levels are 165°,135°,110°,189°, 91°. Hence, the obtuse angle degree lies within the arrays from 90° to less than 180°.


Examples of Obtuse Angles


We understand that angles measuring higher than 90° and also less 보다 180° are referred to as obtuse angles. Therefore, angle that measure up 145°,150°,178°,149°, 91° are thought about as obtuse angle examples. Here are part real-life examples of obtuse angles. Deserve to you observe the obtuse angle in all these images? deserve to you think of an ext objects in genuine life that incorporate obtuse angles?

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Obtuse edge of a Triangle


When one of the vertex angles of a triangle is higher than 90°, the is dubbed an obtuse triangle. An obtuse triangle have the right to either be an isosceles or a scalene triangle. An it is intended triangle cannot be obtuse. The side opposite to the obtuse edge in the triangle is the longest next of that triangle. Similarly, a triangle deserve to never it is in a right angle and also an obtuse angle at the very same time as per the edge sum home of a triangle. Thus, we can conclude the if one of the angles of a triangle is obtuse, then the various other two angle of a triangle need to be acute angles.

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The triangles above have one angle higher than 90°. Hence, lock are called obtuse-angled triangles or just obtuse triangles. In an obtuse triangle, the amount of the squares of the two sides is much less than the square that the longest side. In ΔABC, the sides measure a,b,c such that c is the biggest side, thus: a2 + b2 2. Whereas if in a triangle, if a2 + b2 2, then the triangle is one obtuse triangle.


Obtuse angle of a Rhombus


A rhombus is a special kind of square which includes:

four same sidestwo pairs of parallel sidesequal opposite angles

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The sum of the internal angles of any quadrilateral is 360°. In a rhombus, consecutive angles are supplementary and also opposite angles space equal. Thus, at any type of given time, a rhombus has two obtuse angle that space equal and also the various other two angles space acute and also they are likewise equal.


Obtuse angle of a Parallelogram


A parallelogram is a special form of quadrilateral which includes:

two pairs of parallel sidesopposite sides of equal lengthsequal opposite angles

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The amount of the internal angles of any type of quadrilateral is 360°. In a parallelogram, continually angles are supplementary and also opposite angles are equal. Thus, at any given time, a parallelogram has two obtuse angle that room equal and also the various other two angles room acute and they are also equal.

Important Notes

All angle measuring much more than 90° and less than 180° are called obtuse angles.In one obtuse triangle, the amount of the squares of the 2 sides is much less than the square of the longest side.

Thinking the end Of the Box!

Can a triangle have more than one obtuse angle?Which polygon has all its inner angles as obtuse angles?Can there be a parallel without one obtuse angle? If so, what shape have the right to it be?

Topics concerned Obtuse Angles

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


Obtuse edge Examples


Example 1: determine the obtuse angle from the complying with figures.

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Solution:

Option (b) and option (c) are an ext than 90° and also less 보다 180°. Therefore, they space obtuse angles. Alternative (b) and also option (c) space obtuse angles.


Example 2: in ~ what times, in the clocks displayed below, one obtuse angle is formed?

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Solution:

We have the right to observe the in every instances, an obtuse edge is formed in between the hour's hand and the minutes' hand of the clock.

At 5:00, the hour hand is at 5 and the minute hand is in ~ 12. So, by observation, we have the right to conclude the the angle formed is better than 90º yet less 보다 180º, i beg your pardon is one obtuse angle. Using a protractor, we can confirm that it is do an angle between (90º come 180º), therefore it is an obtuse angle.At 8:00, the hour hand is in ~ 8 and the minute hand is in ~ 12. So, through observation, we have the right to conclude the the angle developed is higher than 90º however less 보다 180º, which is one obtuse angle. Using a protractor, we deserve to confirm that it is make an angle in between (90º to 180º), hence it is one obtuse angle.At 10:15, the hour hand is at 10 and the minute hand is at 3. So, through observation, we have the right to conclude the the angle developed is higher than 90º yet less 보다 180º, i m sorry is an obtuse angle. Using a protractor, we deserve to confirm that it is make an angle between (90º come 180º), thus it is an obtuse angle.At 2:40, the hour hand is slightly above and the minute hand is in ~ 8. So, by observation, we can conclude that the angle created greater than 90º yet less 보다 180º, which is an obtuse angle. Using a protractor, we deserve to confirm that it is make an angle between (90º to 180º), thus it is one obtuse angle.

Therefore, one obtuse edge is created at 5:00, 8:00, 10:15, and also 2:40.

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Example 3: can an obtuse angle triangle have sides measure 4 units, 5 units, and also 8 units?

Solution:

In one obtuse triangle, the sum of the square of 2 sides should be much less than the square the the biggest side i.e a2 + b2 2 where c is the biggest side. Permit a = 4 units, b = 5 units, c = 8 devices (largest side) ⇒ a2 = 16, b2 = 25, c2 = 64 ⇒ a2 + b2 = 16 + 25 = 41. Because 41 2 + b2 is less than c2. Hence, the given measures form an obtuse angle triangle. Therefore, the sides measuring 4 units, 5units and 8 units kind an obtuse triangle.