How Many Radians Is 270

270 Degree Angle

Angles are defined as the measurement of opening at the intersection point of two lines or rays. 270-degree angle is an angle that is greater than a straight angle and is hence known as a reflex angle. Nosotros will be learning about the 270-degree angle drawing and conversion in this article.

1.	What is a 270 Degree Bending?
2.	270 Degree Angle Name
3.	270 Degree Angle in pi
4.	How to Construct 270 Degree Angle?
5.	FAQs on 270 Degree Angle

What is a 270 Degree Bending?

270-degree bending also represented as 270° is an bending that is greater than a directly angle. Any angle that is greater than 180º is known as a reflex angle. Therefore, 270º is a reflex angle. Nosotros can also define 270-degree angle as 3 right angles considering 270° is a multiple of 90º, i.e., it tin can exist expressed every bit 270º = 3 × 90º.

A 270º angle can be easily measured using a protractor by subtracting the internal angle from 360º. Nosotros tin run into a 270-degree bending is formed betwixt the hands of a clock at 9 o'clock.

270 Degree Bending Proper name

270-degree bending is also known as a reflex angle as it is greater than 180 degrees but lesser than a 360-degree angle. Permit us look into the 270° angle representation on a unit circumvolve past anticlockwise rotation.

We start from signal A, moving in the anticlockwise direction past three xc° to land on point D giving the states 270°. This is because 90° × 3 = 270°.

Steps to draw 270-Degree Angle using a Protractor

Let u.s.a. depict a 270-degree bending using a protractor forth with the steps equally described below.

Step ane:
The protractor is exactly placed at the center aligning with the 0º line and a line is drawn besides known equally the reference line.
Stride 2:
The counting of the angle is done from 0º to 180º in the anticlockwise direction, and going up to another 90° angle from the bespeak where it ended at 180° to make it a 270° angle.
Step 3:
We marker this signal and join it with the heart. Hence the reflex of this angle taken in the anticlockwise direction gives us 270°.

270 degree angle

To measure out reflex angle XYZ, follow the steps given below.

Pace 1:
Identify the center of the protractor exactly at the eye colliding with the 0° line. This is the reference line YZ.
Step two:
Now expect for the indicate where 180° completes starting from the reference line YZ and marker information technology.
Step 3:
Now mensurate the extra part of the angle starting from 180° to the second line XY. Hither the extra function is equal to ninety°.
Step iv:
Once the bending beyond 180° is measured, add it to 180° to get the reflex angle that is required. Hence, we get the value 180° + 90° = 270°. Therefore the reflex angle XYZ = 270°.
Step 5:
For verification, we measure the interior angle XYZ and subtract it from 360° to check if nosotros are getting the aforementioned result. Here the interior angle XYZ = xc°. Thus, reflex XYZ = 360° – xc° = 270°.

270 Degree Angle in pi

Let us convert the 270-degree angle to radian in terms of pi or π. According to the caste to radian conversion rule, we use this formula = Degree measure × (π/180°). Therefore, 270° = 270° × (π/180°) radian = 3π/ii radian. Too, 1° = (π)/180 radians = 0.017453 radians. Therefore, 270° = 270° × 0.017453 = 4.71239 radians.

Thus, the 270-degree bending is equal to 3π/ii radians or 4.71239 radians.

How to Construct 270 Caste Bending?

We know that 270 degrees = 360 degrees – xc degrees. Therefore, we will first construct a ninety degree angle using a compass and ruler and observe the reflex of that angle which volition be the 270 degree angle. Nosotros will be looking into the steps to construct a 270-degree bending as described below.

Step i:
Depict a ray AB using a ruler.
Step 2:
Put the indicate of the compass at A and draw an arc that cuts the line AB and mark that cutting signal as C.
Footstep 3:
Put the point of the compass at C and draw an arc of radius Air conditioning that cuts the arc drawn in Footstep two and marker the intersection betoken every bit D.
Step iv:
Keeping the compass at D, draw an arc of radius AC using a compass to cut the arc drawn in Step two and marker the intersection point as Eastward.
Stride five:
Keeping the compass at point D, draw another arc using the same radius AC between points D and E.
Step 6:
At present keeping the compass at indicate E, draw some other arc using the same radius Air-conditioning to cut the arc drawn in step 5 and marker the intersection point as F.
Step vii:
Bring together F and A. The angle FAB is a 90-degree bending.
Step 8:
The reflex angle FAB volition exist equal to the full bending-bending FAB, i.eastward., reflex angle FAB = 360° – 90° = 270°. Thus, reflex angle FAB is the required angle of 270 degrees.

270 degree angle construction

270 Degree Bending Examples

Instance 1: What is the value of 2 times of 270 degree angle in terms of radians?

Solution:
Nosotros know that 270-caste angle = 4.71239 radians.

Therefore, 2 × 270 degree angle = ii × four.71239 radians = 9.42478 radians.

Thus, the value of ii times of 270-degree angle in terms of radians is 9.42478 radians.
Example two: Notice the value of ∠AOB, if reflex ∠AOB = 270° in the given diagram.

Solution:
Given reflex ∠AOB = 270 degree angle.

Thus, ∠AOB = 360° – reflex ∠AOB

= 360° – 270°

= 90º

Therefore, the value of ∠AOB is equal to 90°.

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Practice Questions on 270 Degree Angle

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FAQs on 270 Degree Angle

What is a 270 Degree Bending?

A 270-caste angle, too represented every bit 270º, is a reflex bending since it is greater than 180º. Information technology is made upwardly of 3 right angles. Information technology tin be represented on a unit circumvolve and tin exist shown using a protractor too.

How to Describe a 270 Degree Angle with a Protractor?

A 270-degree angle tin can be drawn using a protractor past following the steps described. The protractor is exactly placed at the center aligning with the 0º line and a line is drawn also known as the reference line, followed by counting the angle from 0º to 180º in the anticlockwise direction, and going upwardly to another xc° angle from the bespeak where it concluded at 180º to brand it a 270º angle. We marking this point and join it with the eye. Hence the reflex of this angle taken in the anticlockwise direction gives the states 270º.

How many Right Angles make 270 Degree Angle?

A 270º angle has 3 right angles. This is because 270 is a multiple of 90 i.e., 270° = 3 × xc°.

What is a 270 Degree Angle called?

A 270-degree angle is called a reflex bending because it is greater than a straight angle or 180° and less than a complete angle (360 degrees).

What does a 270 Caste Angle wait like?

A 270-degree angle can exist divers as 3 times of a right bending or 3/4th part of a full angle since (3/4) of 360° is equal to 270º. Hence, to plot a 270-caste bending we become about 3/4 rotation of the central angle. 270-caste angle looks like 3 quarters of a circle since each quarter has an angle of 90º, thus iii quarters will exist 3 × ninety° = 270°.

How to Catechumen 270 Caste Angle to Radian Measure in Terms of pi?

To convert 270 degrees to radian measure in terms of pi, we will multiply 270º with (π/180°) that will exist (270 × π) / 180 = (3π/2) radians.