Angles are an essential concept in geometry that helps us understand the relationships and measurements of lines and shapes. Most of us are familiar with the concept of right angles, which measure exactly 90 degrees. But what about angles beyond 90 degrees? Well, these angles are called obtuse angles.

Exploring Angles Beyond 90 Degrees

Obtuse angles are any angles greater than 90 degrees but less than 180 degrees. In other words, they are wider or “more open” than right angles, but not as wide as straight angles.

To visualize an obtuse angle, imagine a clock. The hands of the clock at any time form an angle. When the hands indicate 3 o’clock, they form a right angle. As we move towards 4 o’clock and beyond, the angle formed becomes obtuse until it reaches 180 degrees at 6 o’clock, which is a straight angle.

Obtuse angles can be identified visually by their wider opening. They tend to look like an opening door or a “V” shape.

Properties of Obtuse Angles

Obtuse angles possess several interesting properties. Let’s explore some of them below:

  • Obtuse angles can never be acute angles, which are angles less than 90 degrees.
  • The sum of an obtuse angle and an acute angle (less than 90 degrees) will always result in a straight angle (180 degrees). For example, if you have a 100-degree obtuse angle and add a 70-degree acute angle to it, they will form a straight angle of 180 degrees.
  • An obtuse angle can be bisected (divided into two equal parts) using a protractor or geometric constructions. The bisector of an obtuse angle will always result in two smaller obtuse angles.

Real-World Examples of Obtuse Angles

Obtuse angles are found everywhere in our daily lives. Here are a few examples:

  • When you open a door wide, the angle between the door and the wall is an obtuse angle.
  • The angle between two walls in the corner of a room is often an obtuse angle.
  • When you kick a ball high into the sky, the angle at which it leaves the ground is an obtuse angle.

In Conclusion

Obtuse angles are angles greater than 90 degrees but less than 180 degrees. They are wider or “more open” than right angles and can be identified by their wide opening similar to a “V” shape. These angles possess interesting properties and can be found in various real-world scenarios. Understanding obtuse angles helps us analyze and appreciate the complexities of geometry and the world around us.

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