An angle is called a Reflex Angle if it varies from more than 180 degrees to less than 360 degrees. We get the word angle from the Latin word “Angulus.”
An angle is formed when two rays at a common point join with each other, this common point is called the node or vertex, and the two rays are called the arms of the angle. The symbol ‘\(\angle\)’ represents the angle.
The angle is measured in degrees using a protractor.
The \(30^\circ, 45^\circ, 60^\circ, 90^\circ, \) and \( 180^\circ\) are most commonly used. Types of angles depend on their values in degrees.
We also represent angles in radians, i.e., in terms of pi (\(\pi\)). Here, 180 degrees is equal to \( \pi\) in radians.
Coming to types of angles:
1. All angles measuring between \(0^\circ\) to \(90^\circ\) are called Acute Angles.
2. \(90^\circ\) is called a Right Angle.
3. Angles measuring between \(90^\circ\) and \(180^\circ\) are called Obtuse Angles.
4. \(180^\circ\) is called a Straight Angle.
5. Angles measuring between \(180^\circ\) and \(360^\circ\) are called Reflex Angles.
Here, we will learn about reflex angles.
A reflex angle varies from 180 degrees to less than 360 degrees. For example, \(300^\circ\)
Measuring Reflex Angles
We can measure Reflex angles in two ways.
- We use a protractor which is made to measure reflex angles.
- Measuring the acute side or interior side and subtracting it with \(360^\circ\).
Where do we find Reflexive angles?
We can find a reflexive angle in
- The arms of the clock sometimes form reflexive angles on certain readings.
- Chinese fan, it opens up more than \(180^\circ\).
- If we cut a slice of cake at an acute angle, we find the rest of the cake forms a reflexive angle, etc.
Q. What is reflexive angle for \(120^\circ\)?
The reflexive angle for \(120^\circ\) is\(360^\circ – 120^\circ = 240^\circ\)
Q. Find reflexive angle for \(133^\circ\).
Reflexive angle for \(133^\circ\) is\(360^\circ – 133^\circ = 227^\circ\)
Angles measuring between \(180^\circ and 360^\circ\) are called reflex angles.
As the total sum of all angles in a triangle is \(180^\circ\), it is impossible to have a reflexive angle in a triangle.
\(360^\circ\) is known as the wide angle.
\(180^\circ\) is known as the straight angle.
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