270 Degree Angle - Construction, In Radians, Examples - Cuemath

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.

• Protractor
• Right Angle
• Reflex Angle
• Degrees to Radians
• 360 Degree Angle
• 30 Degree Angle
• 90 degree-angle