What Is a Reflex Angle?

How to read the larger opening

That is why reflex angles often need explicit wording. If a problem simply names angle ABC without saying reflex, many readers assume the smaller angle is intended. The label matters because two different measures can share the same rays.

Reflex angles are useful in rotation, bearings, and advanced diagram reading because they train students to think beyond the nearest interior region and to name the intended turn precisely.

The same two rays can create a small angle and a reflex angle. If the small opening is 80 degrees, the turn around the other side is 280 degrees. Together they make a full rotation. The wording and the direction of the curved mark tell you which one the problem wants.

When you read a reflex angle, trace the arc slowly from the starting ray to the finishing ray. Do not let your eyes jump to the shorter route. The measure describes the path of the turn, not just the final position of the rays.

• A reflex angle measures more than 180 degrees and less than 360 degrees.
• A reflex angle is larger than a straight angle but smaller than a full rotation.
• It is measured around the outside of the smaller interior angle formed by the same rays.
• A reflex angle usually needs to be identified explicitly so it is not confused with the smaller interior angle.

Where reflex angles appear

• Use reflex-angle language in rotation problems, bearings, and turn-based geometry discussions.
• Use it when one pair of rays creates both a smaller interior angle and a larger outside turn.
• Use it in advanced diagram reading where the intended measure is the longer route around the vertex.

Three reflex-angle checks

• Do not read the smaller interior opening and assume that is always the requested angle.
• Do not call any angle over ninety degrees reflex; it must exceed one hundred eighty degrees.
• Do not forget to specify reflex when the same rays could also describe a much smaller angle.