Calculate reflex and primary angles, convert degrees, radians, and DMS, and find arc length and sector area from radius and angle.

Signed angles are normalized only when identifying primary/reflex angles.

Reflex Angle Formula

RA = 360^ยฐ - PA

Variables:

  • RA is the Reflex Angle (degrees)
  • PA is the primary (interior) angle (degrees)

To calculate Reflex Angle (for a primary interior angle PA with 0ยฐ < PA < 180ยฐ), subtract the primary angle from 360ยฐ.

How to Calculate Reflex Angle?

The following steps outline how to calculate the Reflex Angle.

  • First, determine the primary (interior) angle (degrees). 
  • Next, gather the formula from above = RA = 360ยฐ โˆ’ PA.
  • Finally, calculate the Reflex Angle.
  • After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Primary angle (degrees) = 40, so Reflex angle (degrees) = 360 โˆ’ 40 = 320.

FAQs

What is a Reflex Angle?

A reflex angle is an angle that measures more than 180 degrees and less than 360 degrees. It is the larger angle between two rays that share a common endpoint.

How do you differentiate between a Reflex Angle and an Obtuse Angle?

An obtuse angle measures more than 90 degrees but less than 180 degrees, whereas a reflex angle measures more than 180 degrees but less than 360 degrees.

Can a Reflex Angle be negative?

In standard geometry, a reflex angle is usually defined as a positive angle between 180ยฐ and 360ยฐ, so it is not negative. In other contexts (like directed angles in trigonometry), angles can be negative, but you would typically convert to a positive coterminal angle (between 0ยฐ and 360ยฐ) before calling it โ€œreflex.โ€

Why is it important to calculate Reflex Angles?

Calculating reflex angles is useful in fields like engineering, architecture, navigation, and mathematics, where you may need the larger rotation/turn between two directions.