What Is The Measure Of

In geometry, the measure of rotation of a given ray about its initial point is called angle. The principal ray is called the initial side, and the last position of the ray subsequently rotation is called the terminal side of the bending. The point of rotation is called the vertex. The angle is positive if the direction of rotation is anticlockwise, whereas the angle is negative if the direction of rotation is clockwise. The measure of an bending is the corporeality of rotation made to get the terminal side from the initial side. There are many units for measuring angles, such as degree measure and radian measure. In this article, you lot will acquire what caste measurement is and how to go the degree measurement of an angle with examples.

Degree Measure of an Angle

The caste measure is represented using "°" and is called a degree symbol. The measure of an angle is said to be one degree, i.e. i°, if the rotation from the initial side to the terminal side is (one/360)th of a revolution equally one complete revolution means the initial and final sides coincide. In other words, an angle equal to 360 degrees is called full rotation or full angle. It is formed when i of the arms makes a complete rotation to form an bending. The below effigy shows the degree measure of an angle at different positions.

Degree measure of an angle

Here, OA is the initial side and OB, OC, OD, OE, OF, OG, OH, OI, OJ, OK, OL, OM, ON, OP, OQ and OR are last sides each of which measure certain angles. However, the initial side OA and terminal side OQ coincide with each other later 1 complete revolution. Thus, it made an bending of 360 degrees.

Caste Mensurate Formula

Some of the of import facts about the degree measure are:

A degree is divided into 60 minutes, and a infinitesimal is divided into 60 seconds.
One sixtieth of a degree is called a minute, written as 1′.
I sixtieth of a minute is called a second, written as 1″.

The above statements can be written equally:

1° = threescore′ (i degree = lx minutes)

one′ = 60″ (i minute = threescore seconds)

(1/60)° = 1′ (I sixtieth of a degree = One minute)

(i/threescore)′ = ane″ (One sixtieth of a minute = Ane second)

Degree Measure Tool

The protractor is one the geometric tools, used to measure the degree of an bending. The below points should be remembered while measuring an angle using the degree measurement tool, i.eastward. protractor.

If the angle is to exist measured from the left side of the protractor, nosotros accept to consider the outer reading provided on the protractor.
If the angle is measured from the protractor's right side, nosotros have to consider the inner reading provided on the protractor.

Some of the angles and their measurements using a protractor are given below to understand the concept in a improve way.

Example i: Measure out the angle of lx degrees.

In the below effigy, the angle is measured in degrees from the right side of the protractor. Thus, ∠ABC = 60 °

Degree measure of 60 degrees

If nosotros measure the bending from the left side of the protractor, and so ∠CBD = 120°. As we can discover that ∠ABC and ∠CBD accept the same last side and their initial sides are the segments of the ray AB. The bending measure out is different from one some other because of the way we consider the reading.

Example ii: What is The caste Measure out of a Directly Angle

The caste mensurate of a straight bending is 180 degrees, and this tin can be shown as:

Degree measure of 180 degrees

Example 3: Show the 250 degrees measure of an angle.

Let u.s.a. write the angle 250 degrees as the sum of two angles so that we can easily mark the angle using a protractor.

250° = 180° + 70°

And so, starting time, nosotros need to rotate the protractor for 180 degrees and so mensurate 70 degrees. This is given in the figure beneath.

Degree measure of 250 degrees

Similarly, we tin observe the degree measure out of an arc and central angle. Besides, learn the measurement of angles with examples hither.

Degree Measure of one Radian

Another unit for the measurement of an bending is the radian measure. All the same, both degree and radian measures can be converted from one unit to another. The caste measure out of one radian is given by:

1 radian = 180°/π = 57°16′ (approx)

The above relation is used to convert the measurement of angles from degrees to radians and vice versa.