Obtuse angle is one of the varieties of angle that type on the aircraft surface. In Geometry, one obtuse angle is an angle that is higher than 90° and less than 180°. Often throughout a day in a 24 hrs duration, we have the right to see a clock framing plenty of obtuse angle degrees in between a minute hand and also an hour hand. Let us learn much more about the obtuse angle and also 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 angle of a Rhombus
6.Obtuse angles of a Parallelogram
7.FAQs on Obtuse Angle

What Is one Obtuse Angle?


The an interpretation of one obtuse angle in Geometry says that an edge whose measure is higher than 90° and also less 보다 180° is referred to as an obtuse angle. In other words, one obtuse angle is an angle in between a ideal angle and a straight angle.

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Obtuse edge Degree


In the above section, we check out that one angle the measures much less than 180 degrees and much more than 90 levels angle. The instances 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 the Obtuse Angles


We recognize that angle measuring higher than 90° and less 보다 180° are dubbed obtuse angles. Therefore, angle that measure up 145°,150°,178°,149°, 91° are considered as obtuse angle examples. Here are part real-life instances of obtuse angles. Deserve to you watch the obtuse angle in every these images? deserve to you think of an ext objects in real life that encompass obtuse angles?

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Obtuse angle of a Triangle


When among the vertex angles of a triangle is higher than 90°, it is called an obtuse triangle. An obtuse triangle can either it is in an isosceles or a scalene triangle. An it is provided triangle cannot be obtuse. The side opposite to the obtuse angle in the triangle is the longest side of that triangle. Similarly, a triangle deserve to never it is in a right angle and also an obtuse angle at the exact same time together per the edge sum residential or commercial property of a triangle. Thus, we have the right to conclude that if one of the angle of a triangle is obtuse, climate the other two angles of a triangle need to be acute angles.

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


Obtuse angles of a Rhombus


A rhombus is a special type 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, continuous angles space supplementary and opposite angles room equal. Thus, at any given time, a rhombus has two obtuse angle that are equal and the other two angles space acute and also they are likewise equal.


Obtuse angle of a Parallelogram


A parallel is a special form of quadrilateral which includes:

two pairs of parallel sidesopposite sides of equal lengthsequal the contrary angles

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

Important Notes

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

Thinking out Of the Box!

Can a triangle have an ext than one obtuse angle?Which polygon has all its inner angles as obtuse angles?Can over there be a parallelogram without one obtuse angle? If so, what shape deserve to it be?

Topics regarded Obtuse Angles

Check out couple of more interesting write-ups related come the obtuse angle and its properties.


Obtuse edge Examples


Example 1: determine the obtuse angles from the following figures.

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Solution:

Option (b) and also option (c) are more than 90° and less 보다 180°. Therefore, they space obtuse angles. Choice (b) and option (c) room obtuse angles.


Example 2: in ~ what times, in the clocks shown below, an obtuse edge is formed?

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Solution:

We have the right to observe the in all instances, an obtuse angle is formed in between the hour's hand and also the minutes' hand that the clock.

At 5:00, the hour hand is at 5 and the minute hand is in ~ 12. So, by observation, we can conclude that the angle developed is greater than 90º but less than 180º, i beg your pardon is one obtuse angle. Using a protractor, we can confirm that it is making an angle between (90º to 180º), therefore it is one obtuse angle.At 8:00, the hour hand is at 8 and also the minute hand is at 12. So, through observation, we can conclude the the angle formed is better than 90º but less than 180º, i beg your pardon is an obtuse angle. Making use of a protractor, we can confirm the it is making an angle 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 that the angle developed is better than 90º but less than 180º, i beg your pardon is an obtuse angle. Making use of a protractor, we deserve to confirm the it is do an angle in between (90º to 180º), hence it is one obtuse angle.At 2:40, the hour hand is slightly over and the minute hand is at 8. So, by observation, we can conclude that the angle created greater 보다 90º but less than 180º, i beg your pardon is an obtuse angle. Making use of a protractor, we have the right to confirm that it is do an angle between (90º to 180º), for this reason it is one obtuse angle.

Therefore, one obtuse angle is created at 5:00, 8:00, 10:15, and 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 amount of the square of two sides have to be less than the square of the greatest side i.e a2 + b2 2 whereby c is the biggest side. Let a = 4 units, b = 5 units, c = 8 units (largest side) ⇒ a2 = 16, b2 = 25, c2 = 64 ⇒ a2 + b2 = 16 + 25 = 41. Due to the fact that 41 2 + b2 is much less than c2. Hence, the given measures kind an obtuse angle triangle. Therefore, the sides measuring 4 units, 5units and 8 units type an obtuse triangle.