Obtuse Angle
Obtuse angle is one of the types of angles that form on the plane surface. In Geometry, an obtuse angle is an angle that is greater than 90° and less than 180°. Often during a day in a 24 hours duration, we can see a clock framing many obtuse angle degrees between a minute hand and an hour hand. Let us learn more about the obtuse angle and it's properties.
| 1. | What Is an Obtuse Angle? |
| 2. | Obtuse Angle Degree |
| 3. | Examples of Obtuse Angles |
| 4. | Obtuse Angle of a Triangle |
| 5. | Obtuse Angles of a Rhombus |
| 6. | Obtuse Angles of a Parallelogram |
| 7. | FAQs on Obtuse Angle |
What Is an Obtuse Angle?
The definition of an obtuse angle in Geometry states that an angle whose measure is greater than 90° and less than 180° is called an obtuse angle. In other words, an obtuse angle is an angle between a right angle and a straight angle.
Obtuse Angle Degree
In the above section, we read that an angle that measures less than 180 degrees and more than 90 degrees angle. The examples of obtuse angle degrees are 165°,135°,110°,189°, 91°. Hence, the obtuse angle degree lies within the ranges from 90° to less than 180°.
Examples of Obtuse Angles
We know that angles measuring greater than 90° and less than 180° are called obtuse angles. Therefore, angles that measure 145°,150°,178°,149°, 91° are considered as obtuse angle examples. Here are some real-life examples of obtuse angles. Can you observe the obtuse angles in all these images? Can you think of more objects in real life that include obtuse angles?
Obtuse Angle of a Triangle
When one of the vertex angles of a triangle is greater than 90°, it is called an obtuse triangle. An obtuse triangle can either be an isosceles or a scalene triangle. An equilateral triangle cannot be obtuse. 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 angle sum property of a triangle. Thus, we can conclude that if one of the angles of a triangle is obtuse, then the other two angles of a triangle must be acute angles.
The triangles above have one angle greater than 90°. Hence, they are called obtuse-angled triangles or simply obtuse triangles. In an obtuse 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, thus: a2 + b2 < c2. Conversely, if in a triangle, if a2 + b2 < c2, then the triangle is an obtuse triangle.
Obtuse Angles of a Rhombus
A rhombus is a special type of quadrilateral which includes:
- four equal sides
- two pairs of parallel sides
- equal opposite angles
The sum of the interior angles of any quadrilateral is 360°. In a rhombus, consecutive angles are supplementary and opposite angles are equal. Thus, at any given time, a rhombus has two obtuse angles that are equal and the other two angles are acute and they are also equal.
Obtuse Angles of a Parallelogram
A Parallelogram is a special type of quadrilateral which includes:
- two pairs of parallel sides
- opposite sides of equal lengths
- equal opposite angles
The sum of the interior angles of any quadrilateral is 360°. In a parallelogram, consecutive angles are supplementary and opposite angles are equal. Thus, at any given time, a parallelogram has two obtuse angles that are equal and the other two angles are acute and they are also equal.
Important Notes
- All angles measuring more than 90° and less than 180° are called obtuse angles.
- In an obtuse triangle, the sum of the squares of the two sides is less than the square of the longest side.
Thinking Out Of the Box!
- Can a triangle have more than one obtuse angle?
- Which polygon has all its internal angles as obtuse angles?
- Can there be a parallelogram without an obtuse angle? If so, what shape can it be?
Topics Related to Obtuse Angles
Check out few more interesting articles related to the obtuse angle and its properties.
Obtuse Angle Examples
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Example 1: Identify the obtuse angles from the following figures.
Solution:
Option (b) and option (c) are more than 90° and less than 180°. Therefore, they are obtuse angles. Option (b) and option (c) are obtuse angles.
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Example 2: At what times, in the clocks shown below, an obtuse angle is formed?
Solution:
We can observe that in all instances, an obtuse angle is formed 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 at 12. So, by observation, we can conclude that the angle formed is greater than 90º but less than 180º, which is an obtuse angle. Using a protractor, we can confirm that it is making an angle between (90º to 180º), thus it is an obtuse angle.
- At 8:00, the hour hand is at 8 and the minute hand is at 12. So, by observation, we can conclude that the angle formed is greater than 90º but less than 180º, which is an obtuse angle. Using a protractor, we can confirm that it is making an angle between (90º to 180º), thus it is an obtuse angle.
- At 10:15, the hour hand is at 10 and the minute hand is at 3. So, by observation, we can conclude that the angle formed is greater than 90º but less than 180º, which is an obtuse angle. Using a protractor, we can confirm that it is making an angle between (90º to 180º), thus it is an obtuse angle.
- At 2:40, the hour hand is slightly above and the minute hand is at 8. So, by observation, we can conclude that the angle formed greater than 90º but less than 180º, which is an obtuse angle. Using a protractor, we can confirm that it is making an angle between (90º to 180º), thus it is an obtuse angle.
Therefore, an obtuse angle is formed at 5:00, 8:00, 10:15, and 2:40.
FAQs on Obtuse Angle
What is an Obtuse Angle in Geometry?
In geometry, we read about various types of angles. Each type of angle has its own characteristic with the help of which we can identify it. Similarly, an obtuse angle is an angle that is always less than 180 degrees and is greater than 90 degrees.
What does an Obtuse Angle Look Like?
The angles measuring greater than 90° and less than 180° are called obtuse angles in geometry. The obtuse angle 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 hand of a clock at 10:15 AM.
How Do You Create an Obtuse Angle?
The definition of an obtuse angle in Geometry states that an angle larger than 90° but less than 180° is called an obtuse angle. We can use a protractor and mark any angle between 90° and 180° to make an obtuse angle.
What Are Some Examples of Obtuse Angles?
145°,150°, 178°, 149°, 91° are all examples of obtuse angles as they are more than 90° and less than 180°.
How Do You Determine an Obtuse Angle?
The definition of an obtuse angle states that if an angle measures more than 90° and less than 180°, it is an obtuse angle. We can use a protractor and verify the same.
What Are the Properties of the Obtuse-angled Triangle?
Given below are the properties of an Obtuse Angled Triangle Properties
- In a triangle, the sum of the two angles except the obtuse angle is less than 90 degrees.
- The side opposite to the obtuse angle in a triangle is the longest side of the triangle.
- An obtuse triangle can have one and only one obtuse angle to satisfy the angle sum property of the triangle.
Can 2 Obtuse Angles be Supplementary?
Two obtuse angles, each measuring greater than 90° cannot form a supplementary pair of angles as then the sum will be greater than 180° which doesn't satisfy the definition of supplementary angles.