What is an Angle?
When two lines or rays meet at a point, an angle is formed. The common point is called the vertex of the angle and the two lines or rays are called the sides or arms of the angle.
An angle is represented by the symbol, ‘∠’.
The angle formed by the rays AB and BC can be written as ‘∠ABC’ or ‘∠CBA’ or ‘∠B’
Here B is the vertex of the angle formed.
Types of Angles
We can classify the angles on the basis of their measurement.
- Acute Angle: Angles that measure less than 90°. For example, 45°.
- Right Angle: An angle that is equal to 90°.
- Obtuse Angle: Angles that are greater than 90° and less than 180°.
- Straight Angle: An angle that measures 180°.
- Reflex Angle: Angles measuring greater than 180° and less than 360°.
- Complete Angle: An angle that is equal to 360°.
What is an Obtuse Angle?
An angle that is greater than 90° but less than 180° is referred to as an ‘obtuse angle’. In other words, an angle between 90° to 180° is an obtuse angle.
The smaller angle in the illustration is known as the obtuse angle, and the bigger angle is known as the reflex angle.
Obtuse Angle Definition
According to the definition, an obtuse angle is any angle with a measure greater than 90° and less than 180°.
Examples of obtuse angles include 166°, 121°, 110°, 117°, 91°.
Obtuse Angles in Real Life
Here are a few instances of obtuse angles in real life. Can you spot the obtuse angles in each of these pictures? Are there any objects in daily life that have obtuse angles?
Here are a few more instances of obtuse angles in real life:
- The angle formed by the hour and minute hands of a clock at seven o’clock
- The inclination at which a laptop’s screen and the keyboard meet
- Angles created by the blades of a ceiling fan
- Angle on a clothes hanger
Rapid Recall
Solved Obtuse Angles Examples
Example 1: Find the obtuse angles in the following image.
Solution:
From the angles shown in the image, the angle formed in option (3) is more than 90° and less than 180°. Therefore, it is an obtuse angle.
(It seems like the angles in option 1 and option 4 are less than 90°. So, they are acute angles. Option 2 is an angle equal to 90° so this is a right angle).
Example 2: Find the obtuse angle(s) in the following options.
Solution:
From the above figures, the angles formed in option (1) and option (2) are more than 90° and less than 180°. Therefore, they are obtuse angles.
Example 3: Find the obtuse angles that the clock hands produced at the times shown below.
Solution:
- The second clock is at 4:46, the hour hand is four divisions ahead of 4, and the minute hand is one division after 9. Therefore, based on our observations, we may say that the angle is obtuse because it is larger than \(90^{\circ}\) but less than 180°.
- The sixth clock is at 12:43, the hour hand is at four divisions after 12, and the minute hand is at three divisions after 8. Therefore, based on our observations, we may say that the angle is obtuse because it is larger than \(90^{\circ}\) but less than 180°.
- The eighth clock is at 9:09, the hour hand is one division ahead of 9, and the minute hand is at four divisions after 1. Therefore, based on our observations, we may say that the angle is obtuse because it is larger than \(90^{\circ}\) but less than 180°.
When two rays or lines overlap each other, the angle formed is zero degrees. It is also called zero angle.
Angles have a measurement greater than 180 degrees but less than 360 degrees are called reflex angles. Hence an angle measuring 200 degrees is a reflex angle.
Half of a reflex angle is always an obtuse angle.
Obtuse angles are larger than 90°, as is common knowledge. Obtuse angles can be seen in many everyday objects, like hangers used to store clothes, a clock’s hour and minute hands at 5 O’clock, and many other examples.