An angle whose measure is greater than 180 degrees but less than 360 degrees is termed a reflex angle. An acute angle and an obtuse angle will always be shown on the other side of the reflex angle. It is less than a full rotation but more than a straight angle.
|1.||What are Reflex Angles?|
|2.||How to Measure a Reflex Angle?|
|5.||FAQs on Reflex Angle|
What are Reflex Angles?
- Reflex angle = 180° + Acute angle
- Reflex angle = 180° + Right angle
- Reflex angle = 180° + Obtuse angle
An Angle and its Reflex Angle
When two lines intersect at a point, the measure of the “opening” between these two lines is called an “Angle”. Let’s take the letters A, B, and O to name the angle.
In the above image reflex angle is the larger angle, and the smaller angle is an acute angle. It is to avoid this particular ambiguity that we refer to the angle marked outside as reflex ∠AOB.
Note: smaller ∠AOB and its reflex ∠AOB gives a sum of 360°.
Let us check one more example where two different angles can be shown together. Look at the below image showing two angles simultaneously, straight angle 180° completed at dotted green line and reflex angle 210° marked with pink circle.
In the above figures, the angle 210 degree is a reflex angle because it lies between 180° and 360°.
How to Measure a Reflex Angle?
We know that with the help of a protractor we can easily measure any type of angle. Let us look at the following ways to measure the reflex angle.
- Measure the internal angle and subtract it from 360 degrees.
- With the help of a protractor
Steps to measure a reflex angle
To measure reflex angle XYZ, follow the steps given below.
Step 1: Place the center of the protractor at the center point and adjust it with the line that goes through 0°.
Step 2:Now look for the point where 180 degrees completes and mark it.
Step 3:Now measure the rest part of the angle starting from 180 degrees to the second line.
Step 4:Once the angle beyond 180 degrees is measured, now add it to 180° to get the reflex angle that is required.
Step 5:Now check the final measured angle, by measuring the interior angle and subtract it from 360°. This is another way to measure reflex angles and can also be effectively used for verification.
Related Articles on Reflex Angle
Check out these interesting articles to know more about reflex angle and its related topics.
Example 1: If angle AOB = 57°, what is the size of reflex angle AOB.
Solution: When you add the smaller angle and the reflex angle of the same shape, the resultant is always 360°. Therefore, reflex angle AOB = 360° − 57° = 303°
Example 2: Find the least number of 35° angles, needed to make a reflex angle?
(a) 2 × 35° = 70°, which is between 0° and 90°, so acute angle.
(b) 5 × 35° = 175°, which is between 90° and 180°, so obtuse angle.
(c) 6 × 35° = 210°, which is between 180° and 360°, so reflex angle.
(d) 7 × 35° = 245°, which is also reflex, but we have already found the least number which is 6.
Therefore, option C is correct.
FAQs on Reflex Angle
What is a Reflex Angle?
An angle whose measure is greater than 180 degrees but less than 360 degrees is termed a reflex angle. Reflex angle 180° < x < 360° (Where ‘x’ denotes any angle.)
What are the Examples of Reflex Angle?
All the measuring angles above 180 degrees and less than 360 degrees are termed Reflex angles. For example, 182 degrees, 210 degrees, 310 degrees, etc. Note that 180º and 360º are not reflex angles as they are straight angles and complete angles respectively.
What is a Complete Angle?
An angle that measures 360 degrees is known as the complete angle. It is also known as a full angle.
Is 180 Degrees Angle a Reflex Angle?
No, 180 degrees is not a reflex angle. It is a straight angle. An angle formed by a straight line is called a straight angle. It is one-half of the whole turn of a circle. It is called straight because it appears as a straight line.
What is an Angle in Math?
In plane geometry, an angle is the figure formed by two rays, lines, or line segments, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. An angle is denoted using the symbol ∠.
How Do you Describe Angles?
In plane geometry, an angle can be described as a figure formed by two rays, lines, or line segments meeting at a common endpoint called the vertex of the angle.