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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. We will be learning about the 270-degree angle drawing and conversion in this article.
|1.||What is a 270 Degree Angle?|
|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 Angle?
270-degree angle also represented as 270° is an angle that is greater than a straight angle. Any angle that is greater than 180º is known as a reflex angle. Therefore, 270º is a reflex angle. We can also define 270-degree angle as 3 right angles because 270° is a multiple of 90º, i.e., it can be expressed as 270º = 3 × 90º.
A 270º angle can be easily measured using a protractor by subtracting the internal angle from 360º. We can see a 270-degree angle is formed between the hands of a clock at 9 o'clock.
270 Degree Angle Name
270-degree angle is also known as a reflex angle as it is greater than 180 degrees but lesser than a 360-degree angle. Let us look into the 270° angle representation on a unit circle by anticlockwise rotation.
We start from point A, moving in the anticlockwise direction by three 90° to land on point D giving us 270°. This is because 90° × 3 = 270°.
Steps to draw 270-Degree Angle using a Protractor
Let us draw a 270-degree angle using a protractor along with the steps as described below.
- Step 1: The protractor is exactly placed at the center aligning with the 0º line and a line is drawn also known as the reference line.
- Step 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 point where it ended at 180° to make it a 270° angle.
- Step 3: We mark this point and join it with the center. Hence the reflex of this angle taken in the anticlockwise direction gives us 270°.
To measure reflex angle XYZ, follow the steps given below.
- Step 1: Place the center of the protractor exactly at the center colliding with the 0° line. This is the reference line YZ.
- Step 2: Now look for the point where 180° completes starting from the reference line YZ and mark it.
- Step 3: Now measure the extra part of the angle starting from 180° to the second line XY. Here the extra part is equal to 90°.
- Step 4: Once the angle 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 we are getting the same result. Here the interior angle XYZ = 90°. Thus, reflex XYZ = 360° - 90° = 270°.
270 Degree Angle in pi
Let us convert the 270-degree angle to radian in terms of pi or π. According to the degree to radian conversion rule, we use this formula = Degree measure × (π/180°). Therefore, 270° = 270° × (π/180°) radian = 3π/2 radian. Also, 1° = (π)/180 radians = 0.017453 radians. Therefore, 270° = 270° × 0.017453 = 4.71239 radians.
Thus, the 270-degree angle is equal to 3π/2 radians or 4.71239 radians.
How to Construct 270 Degree Angle?
We know that 270 degrees = 360 degrees - 90 degrees. Therefore, we will first construct a 90 degree angle using a compass and ruler and find the reflex of that angle which will be the 270 degree angle. We will be looking into the steps to construct a 270-degree angle as described below.
- Step 1: Draw a ray AB using a ruler.
- Step 2: Put the point of the compass at A and draw an arc that cuts the line AB and mark that cut point as C.
- Step 3: Put the point of the compass at C and draw an arc of radius AC that cuts the arc drawn in Step 2 and mark the intersection point as D.
- Step 4: Keeping the compass at D, draw an arc of radius AC using a compass to cut the arc drawn in Step 2 and mark the intersection point as E.
- Step 5: Keeping the compass at point D, draw another arc using the same radius AC between points D and E.
- Step 6: Now keeping the compass at point E, draw another arc using the same radius AC to cut the arc drawn in step 5 and mark the intersection point as F.
- Step 7: Join F and A. The angle FAB is a 90-degree angle.
- Step 8: The reflex angle FAB will be equal to the full angle-angle FAB, i.e., reflex angle FAB = 360° - 90° = 270°. Thus, reflex angle FAB is the required angle of 270 degrees.
Related Articles on 270 Degree Angle
Check these articles related to the concept of 270-degree angle in geometry.
270 Degree Angle Examples
Example 1: What is the value of 2 times of 270 degree angle in terms of radians?
Solution: We know that 270-degree angle = 4.71239 radians.
Therefore, 2 × 270 degree angle = 2 × 4.71239 radians = 9.42478 radians.
Thus, the value of 2 times of 270-degree angle in terms of radians is 9.42478 radians.
Example 2: Find 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°
Therefore, the value of ∠AOB is equal to 90°.
FAQs on 270 Degree Angle
What is a 270 Degree Angle?
A 270-degree angle, also represented as 270º, is a reflex angle since it is greater than 180º. It is made up of 3 right angles. It can be represented on a unit circle and can be shown using a protractor as well.
How to Draw a 270 Degree Angle with a Protractor?
A 270-degree angle can be drawn using a protractor by 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 up to another 90° angle from the point where it ended at 180º to make it a 270º angle. We mark this point and join it with the center. Hence the reflex of this angle taken in the anticlockwise direction gives us 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 × 90°.
What is a 270 Degree Angle called?
A 270-degree angle is called a reflex angle because it is greater than a straight angle or 180° and less than a complete angle (360 degrees).
What does a 270 Degree Angle look like?
A 270-degree angle can be defined as 3 times of a right angle or 3/4th part of a full angle since (3/4) of 360° is equal to 270º. Hence, to plot a 270-degree angle we go about 3/4 rotation of the central angle. 270-degree angle looks like 3 quarters of a circle since each quarter has an angle of 90º, thus 3 quarters will be 3 × 90° = 270°.
How to Convert 270 Degree 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 be (270 × π) / 180 = (3π/2) radians.