Obtuse Angle
An obtuse angle is defined as an angle that is greater than 90° and less than 180°. One of the most common obtuse angle examples in real life can be seen in a clock which forms these angles between the minute hand and the hour hand at certain times. Let us learn more about the obtuse angle definition, obtuse angle examples, the obtuse angle degree, and its properties.
| 1. | What is an Obtuse Angle? |
| 2. | Obtuse Angle Degree |
| 3. | Obtuse Angle in Real Life |
| 4. | Obtuse Angle Triangle |
| 5. | Acute and Obtuse Angles |
| 6. | FAQs on Obtuse Angle |
What is an Obtuse Angle?
Obtuse angle means an angle whose measure is greater than 90° and less than 180°. In other words, an obtuse angle is an angle between a right angle and a straight angle. Look at some of the examples of obtuse angles given below.
Obtuse Angle Definition
An obtuse angle is defined as an angle that is more than 90° but less than 180°.
Obtuse Angle Degree
In the above section, we read that an angle that measures less than 180 degrees and more than 90 degrees angle is called an obtuse angle. A few examples of obtuse angle degrees are 165°, 135°, 110°, 179°, 91°, etc. Hence, the obtuse angle degree lies within the range of 90° to 180°.
Obtuse Angles in Real Life
We know that angles measuring greater than 90° and less than 180° are called obtuse angles. Here are some real-life examples of obtuse angles. Can you observe the obtuse angles in all these figures? Can you think of more objects in real life that include obtuse angles?
Some other examples of obtuse angles in real-life are given below:
- The angle between the hour and minute hand of a clock at 4 o'clock.
- The angle between the base of an open laptop and its screen.
- Angles formed by the blades of a ceiling fan.
Obtuse Angle Triangle
When one of the interior angles of a triangle is greater than 90°, it is called an obtuse angle triangle. Here are a few properties of an obtuse angle triangle.
- An obtuse triangle can either be an isosceles or a scalene triangle.
- An equilateral triangle cannot be obtuse because all the angles of an equilateral triangle measure 60° each.
- The side opposite to the obtuse angle in the triangle is the longest side of that triangle.
- As per the angle sum property of a triangle, a triangle can never be a right-angled triangle and an obtuse angle at the same time. 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.
- In an obtuse angle triangle, the sum of the squares of the two sides is less than the square of the longest side. For example, if the sides of an obtuse triangle measure a, b, and c such that c is the largest side, then we have: a2 + b2 < c2. Conversely, if in a triangle, if a2 + b2 < c2, then the triangle is an obtuse triangle.
The triangles shown below have one angle greater than 90°. Hence, they are called obtuse-angled triangles or simply obtuse triangles.
Acute and Obtuse Angles
There are different types of angles based on the measurement. Angles that measure less than 90 degrees are known as acute angles, while the angles greater than 90° but less than 180° are known as obtuse angles. Observe the figure given below which shows acute and obtuse angles.
Now, let us understand the difference between acute angles and obtuse angles with the help of the following table.
| Acute Angle | Obtuse Angle |
|---|---|
| It measures less than 90°. | It measures greater than 90° and less than 180°. |
| A triangle with three acute angles is known as an acute angle triangle. | A triangle with 1 obtuse angle and 2 acute angles is termed an obtuse angle triangle. |
| Examples of acute angles: 56°, 12°, 79°, 43°, etc. | Examples of obtuse angles: 124°, 179°, 150°, 95°, etc. |
Important Notes
- All angles measuring more than 90° and less than 180° are called obtuse angles.
- In an obtuse angle 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?
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Obtuse Angle Examples
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Example 1: Identify the obtuse angles from the following figures.
Solution:
a.) The first figure shows an angle of 40°. Since 40° is less than 90°, it is not an obtuse angle. It is an acute angle.
b.) The second figure shows an angle of 117°. Since 117° is more than 90° but less than 180°, it is an obtuse angle.
c.) The third figure shows an angle of 121°. Since 121° is more than 90° and less than 180°, it is an obtuse angle.
d.) The last figure shows an angle of 185°. Since 185° is more than 180°, it is not an obtuse angle. It is a reflex angle.
Therefore, 117° and 121° are obtuse angles.
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Example 2: Observe the clocks shown below and check the time when the hands form an obtuse angle.
Solution:
We can observe that in all instances, an obtuse angle is formed between the hour hand and the minute 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 180°, which is an obtuse angle. Using a protractor, we can confirm that it is making an angle between 90° and 180°.
- 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 180°. 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 an obtuse angle.
- At 2:40, the hour hand is slightly above 3 and the minute hand is at 8. So, by observation, we can conclude that the angle formed is greater than 90º but less than 180º. Using a protractor, we can confirm that it is making 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 characteristics with the help of which we can identify it. Similarly, an obtuse angle is an angle that is greater than 90° but less than 180°.
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 a.m.
How do you Draw 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 draw an obtuse angle.
What are Some Examples of Obtuse Angles?
145°, 150°, 178°, 149°, 91°, are all examples of obtuse angles because they are more than 90° and less than 180°.
What are the Properties of Obtuse Angles?
The basic properties of an obtuse angle are given below:
- Angles that are more than 90° and less than 180° are obtuse angles.
- Angles that lie between a right and a straight angle.
Can Two Obtuse Angles be Supplementary?
Two obtuse angles, each measuring greater than 90° cannot form a supplementary pair of angles because the sum will be greater than 180°. This will not satisfy the condition of supplementary angles in which the sum of two angles is 180°.
What is an Obtuse Angle Triangle?
A triangle with 1 obtuse angle and the other two acute angles is an obtuse-angled triangle. Although the sum of all three interior angles is 180°.
What is an Acute and Obtuse Angle?
An acute angle measures less than 90° and an obtuse angle is greater than 90° but less than 180°.
How many Degrees is an Obtuse Angle?
The degree of an obtuse angle always lies between 90° to 180°.
What are some Obtuse Angle Examples in Real Life?
A few obtuse angle examples in real life are given below:
- The clock forms an obtuse angle at 10:15 with its hour hand and minute hand.
- A reclining chair forms an obtuse angle.
- A pair of scissors forms an obtuse angle when it is opened wide.
How much does an Obtuse Angle Measure?
An obtuse angle measures more than 90° and less than 180°. For example, 91°, 172°, 160°, and so on are all obtuse angles.