Reflex Angle: Definition, Examples, and How to Calculate It

What is a reflex angle?

A reflex angle is an angle that is more than 180 degrees but less than 360 degrees. It is the larger angle you can measure around a point when two rays make a turn.

Think of a full turn as 360 degrees. If two rays make a smaller inside angle, the reflex angle is the rest of the turn around the outside.

Reflex angle rule

The easiest way to calculate a reflex angle is to subtract the smaller angle from a full turn.

Reflex angle = 360° - smaller angle

How to calculate a reflex angle

Use these steps when you know the smaller angle between the two rays.

Step 1: Find or measure the smaller angle.

Step 2: Subtract that angle from 360°.

Step 3: The answer is the reflex angle.

Example: if the smaller angle is 110°, then the reflex angle is 360° - 110° = 250°.

Angle types chart

Reflex angles are only one type of angle. This chart compares common angle types by size and separates exact angles from ranges between angles.

Use the exact boundary rules: 0° is a zero angle, 90° is a right angle, 180° is a straight angle, and 360° is a full turn.

Acute angles are more than 0° and less than 90°. Obtuse angles are more than 90° and less than 180°. Reflex angles are more than 180° and less than 360°.

When you know the reflex angle first

Sometimes a problem gives the reflex angle and asks for the smaller angle. Use the same full-turn idea, but subtract the reflex angle from 360°.

Smaller angle = 360° - reflex angle

Example: if the reflex angle is 245°, the smaller angle is 360° - 245° = 115°.

How to identify a reflex angle in a diagram

Look for two rays that start from the same endpoint. The smaller angle is usually drawn between the rays, but the reflex angle goes the longer way around the outside.

If the marked turn is more than a straight line but does not complete a full circle, it is a reflex angle. That means it must be greater than 180° and less than 360°.

Measuring a reflex angle with a protractor

Most classroom protractors measure angles up to 180°, so they usually show the smaller angle first. To find the reflex angle, measure the smaller angle carefully and subtract it from 360°.

For example, if a protractor shows a smaller angle of 65°, the reflex angle is 360° - 65° = 295°. The protractor did not directly show 295°, but the full-turn rule gives the missing outside angle.

Real-life reflex angle examples

A clock hand can make a reflex angle when you measure the longer turn from one hand to the other. A door that turns far past a straight angle can also show a reflex angle.

Students may also notice reflex angles in rotation arrows, steering turns, playground spinning equipment, and circular diagrams where the larger part of the turn is being measured.

Common mistakes

Do not call 180° a reflex angle. An angle of 180° is a straight angle.

Do not call 360° a reflex angle. A full 360° is a complete turn.

If your answer is less than 180°, you found the smaller angle, not the reflex angle.

Reflex angle questions students should ask

Is the angle larger than a straight angle? If not, it is not reflex.

Is the angle smaller than a full turn? If not, it is 360° instead of reflex.

Do I know the smaller angle? If yes, subtract it from 360° to calculate the reflex angle.

Quick practice

1. Smaller angle = 80°. Reflex angle = 360° - 80° = 280°.

2. Smaller angle = 135°. Reflex angle = 360° - 135° = 225°.

3. Reflex angle = 300°. Smaller angle = 360° - 300° = 60°.