Obtuse angle is just one of the varieties of angles that type on the aircraft surface. In Geometry, one obtuse edge is an angle the is better than 90° and less 보다 180°. Often throughout a job in a 24 hours duration, we deserve to see a clock framing countless obtuse edge degrees in between a minute hand and an hour hand. Let us learn more about the obtuse angle and it's properties.
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|1.||What Is an Obtuse Angle?|
|2.||Obtuse edge Degree|
|3.||Examples of Obtuse Angles|
|4.||Obtuse angle of a Triangle|
|5.||Obtuse angle of a Rhombus|
|6.||Obtuse angle of a Parallelogram|
|7.||FAQs ~ above Obtuse Angle|
What Is an Obtuse Angle?
The an interpretation of one 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 other words, one obtuse edge is one angle between a right angle and a directly angle.
Obtuse edge Degree
In the above section, we review that one angle that measures less than 180 levels and much 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 arrays from 90° to less than 180°.
Examples of Obtuse Angles
We understand that angles measuring greater than 90° and less 보다 180° are referred to as obtuse angles. Therefore, angles that measure up 145°,150°,178°,149°, 91° are considered as obtuse angle examples. Right here are some real-life examples of obtuse angles. Deserve to you watch the obtuse angles in every these images? have the right to you think of an ext objects in genuine life that include obtuse angles?
Obtuse angle of a Triangle
When one of the vertex angle of a triangle is higher than 90°, that is referred to as an obtuse triangle. One obtuse triangle can either it is in an isosceles or a scalene triangle. An it is intended triangle can not be obtuse. The side opposite to the obtuse edge in the triangle is the longest side of the triangle. Similarly, a triangle deserve to never be a best angle and an obtuse angle at the same time together per the edge sum residential property of a triangle. Thus, we can conclude that if among the angles of a triangle is obtuse, then the other two angles of a triangle have to be acute angles.
The triangles over 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 of the two sides is much less than the square that the longest side. In ΔABC, the sides measure up a,b,c such that c is the biggest side, thus: a2 + b2 2. Vice versa, 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 form of square which includes:four same sidestwo bag of parallel sidesequal opposite angles
The amount of the internal angles of any quadrilateral is 360°. In a rhombus, continuous angles room supplementary and opposite angles are equal. Thus, at any given time, a rhombus has actually two obtuse angle that room equal and the other two angles are acute and they are likewise equal.
Obtuse angles of a Parallelogram
A parallelogram is a special form of quadrilateral which includes:two pairs of parallel sidesopposite political parties of same lengthsequal the contrary angles
The sum of the interior angles of any kind of quadrilateral is 360°. In a parallelogram, continually angles are supplementary and opposite angles room equal. Thus, at any given time, a parallelogram has actually two obtuse angle that space equal and the various other two angles space acute and also they are likewise equal.
Important NotesAll angle measuring much more than 90° and also less than 180° are referred to as obtuse angles.In one obtuse triangle, the amount of the squares the the two sides is less than the square that the longest side.
Thinking the end Of the Box!Can a triangle have an ext than one obtuse angle?Which polygon has all its interior angles together obtuse angles?Can over there be a parallelogram without one obtuse angle? If so, what shape deserve to it be?
Topics pertained to Obtuse Angles
Check out couple of more interesting articles related come the obtuse angle and also its properties.
Obtuse angle Examples
Example 1: identify the obtuse angles from the following figures.
Option (b) and also option (c) are an ext than 90° and also less 보다 180°. Therefore, they space obtuse angles. Alternative (b) and option (c) are obtuse angles.
Example 2: at what times, in the clocks shown below, one obtuse edge is formed?
We have the right to observe that in every instances, an obtuse angle is formed in between the hour's hand and the minutes' hand of the clock.At 5:00, the hour hand is in ~ 5 and also the minute hand is in ~ 12. So, by observation, we have the right to conclude the the angle created is higher than 90º however less 보다 180º, i m sorry is one obtuse angle. Using a protractor, we can confirm the it is make an angle in between (90º come 180º), hence it is an obtuse angle.At 8:00, the hour hand is in ~ 8 and the minute hand is in ~ 12. So, by observation, we can conclude the the angle developed is better than 90º but less 보다 180º, i beg your pardon is one obtuse angle. Making use of a protractor, we deserve to confirm that it is make an angle between (90º to 180º), therefore it is one obtuse angle.At 10:15, the hour hand is in ~ 10 and also the minute hand is at 3. So, by observation, we can conclude the the angle formed is higher than 90º however less 보다 180º, i beg your pardon is an obtuse angle. Using a protractor, we have the right to confirm that it is making an angle in between (90º come 180º), therefore it is one obtuse angle.At 2:40, the hour hand is slightly above and the minute hand is in ~ 8. So, by observation, we have the right to conclude that the angle formed greater 보다 90º but less 보다 180º, which is an obtuse angle. Using a protractor, we can confirm that it is do an angle in between (90º come 180º), thus it is one obtuse angle.
Therefore, one obtuse angle is created at 5:00, 8:00, 10:15, and also 2:40.
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Example 3: can an obtuse edge triangle have sides measure up 4 units, 5 units, and 8 units?
In one obtuse triangle, the amount of the square of two sides need to be much less than the square that the biggest side i.e a2 + b2 2 whereby c is the largest 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 much less than c2. Hence, the given measures type an obtuse angle triangle. Therefore, the political parties measuring 4 units, 5units and also 8 units type an obtuse triangle.