As per the Euclidean geometry, the formation of an angle takes place when two rays meet at a common point. These two rays are termed as sides, and the meeting point is called the vertex. Moreover, angles are also formed due to the intersection of two curves, two planes, etc.
A figure showing parts of an angle
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Turn between the two straight lines is called the angle.
Corner point is the vertex.
The two straight lines are arms.
Besides, there are various types of angles you will get to study in Mathematics, but in this discussion, we will put the focus on reflex angles. So, let’s start!
What is a Reflex Angle?
A reflex angle stands always more than 180 degrees and smaller than 360 degrees.
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A reflex angle can be presented as an interval with the help of the following units.
Measurement of a Reflex Angle
In general, when a student is given to measure an angle, the diagram will contain an arc drawn from the joining point. Students can evaluate the angle by directly using a protractor. But a protractor is marked up to 180 degrees, so how can you find a reflex angle?
First, recapitulate reflex angle meaning. In order to make a full 360 turn, an obtuse angle or an acute angle must be added to the reflex angle value.
So, if you are given an acute or obtuse angle measuring x, then full 360 degrees can be achieved with the following expression:
x + r = 360 degrees, here r is the reflex angle.
If the reflex angle is unknown, take ‘x’ on the right-hand side of the equation.
r = 360 – x
This expression is useful in finding out the value of the reflex angle when the obtuse or acute angle is known.
Therefore, when the corresponding obtuse or acute angle is not given, make use of a protractor to find it out. Further, subtract the value from 360 degrees to determine the measurement of a reflex angle.
Other Kinds of Angles
Like as we mentioned earlier about various types of angles, here we have listed the fundamental angles you will study in Mathematics:
Zero Angle
As the name sounds, when an angle is nothing but 0 degrees, it is a zero angle.
Acute Angle
When the angle is lesser than 9 degrees, it is denoted as an acute angle.
Obtuse Angle
When the angle is greater than 90 degrees and less than 180 degrees, they are termed as obtuse angles.
Right Angle
An angle making 1/4th turn or 90 degrees is a right angle and the two lines forming the same are known as perpendicular, normal or orthogonal.
Straight Angle
When an angle is making ½ turn, it is called a straight angle.
Perigon or Complete Angle
A full angle, or perigon or a complete angle makes 360 degrees turn.
Oblique Angle
Oblique angles have sides that are not perpendicular, which means the angle formed is not a right angle or a multiple of it.
Labelling Angles
Students can proceed with two ways to label angles. You can name the angle with a lower-case alphabet like a, b, c, d, etc., or you can use Greek letters like theta or alpha.
On the other hand, you can label an angle with three alphabets where the middle letter denotes the actual angle—for instance, ABC, BAC, CBA, etc.
Do It Yourself
Problem 1. Determine which of the following diagrams are reflex angles.
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Problem 2. Find out which among the following angles is not a reflex angle?
(a) 182 degrees (b) 359 degrees (c) 270 degrees (d) 178 degrees
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FAQs on Reflex Angle
1. How Do Astronomers Evaluate an Object’s Angular Separation?
Ans. Astronomers evaluate an object’s angular separation in the form of degrees. Like for instance, the breadth of sun or moon is 0.5 degrees, the breadth of the little finger is 1 degree at arm’s length, etc. However, these values are based on distinct subjects and must be treated as approximations of the rule of thumb.
2. What is Meant by a Hyperbolic Angle?
Ans. The argument of a circular function is a circular angle; likewise, the argument of a hyperbolic function is a hyperbolic angle. The difference between them can be seen as the opening sizes of both hyperbolic and circular function. The reason being, areas of these two regions stick to the magnitude of angles for both hyperbolic and circular function.
Besides, the hyperbolic angle is not bounded. When they are visualised as infinite series, the circular angles are nothing but forms of hyperbolic alternating series.
3. What is the Definition of the Angle Between 1-D Subspaces?
Ans. In Hilbert space, the angle between one-dimensional subspaces span(u) and span(v) is represented in the form: | {u, v} | = |cos(θ)| ||u|| ||v||. If the provided two subspaces are u and w, and dim(u): = k < equals to dim(w): = l, the definition of k angles can be achieved. It is also termed as principal or canonical angles between subspaces.
4. Which is the Day to Day Reflex Angle Examples?
Ans. In a pie chart having two categories, anyone between them is a reflex angle. But both the categories cannot be 180 degrees each. Secondly, when a person is taking a 360-degree turn, he/she is experiencing through a reflex angle. Another example is 18 hours of sun’s path goes over a reflex angle.