Names of Angles

As the Angle Increases, the Name Changes:

Be Careful What You Measure

Positive and Negative Angles

When measuring from a line:

• a positive angle goes counterclockwise (opposite direction that clocks go)
• a negative angle goes clockwise

Example: −67°

Parts of an Angle

The corner point of an angle is called the vertex

And the two straight sides are called arms

The angle is the amount of turn between each arm.

Labelling Angles

An Acute Angle is less than 90° 

This is an acute angle

All the angles below are acute angles:

Which Angle?

Remember to look carefully at which angle you are being asked to name:

The acute angle is the small angle which is less than 90°.

Right Angles

A right angle is an internal angle which is equal to 90°

This is a right angle

Note the special symbol like a box in the angle. If you see this, it is a right angle. The 90° is rarely written in. If you see the box in the corner, you are being told it is a right angle.

All the angles below are right angles:

A right angle can be in any orientation or rotation as long as the internal angle is 90°

Obtuse Angle 

An Obtuse Angle is more than 90° but less than 180°

This is an obtuse angle !

All the angles below are obtuse angles:

Straight Angle

A straight angle is 180 degrees

This is a straight angle

A straight angle changes the direction to point the opposite way.

Sometimes people say "You did a complete 180 on that!" ... meaning you completely changed your mind, idea or direction.

All the angles below are straight angles: 

Reflex Angles

Different Angles have different names: 

A Reflex Angle is more than 180° but less than 360°

This is a reflex angle

All the angles below are reflex angles:

Which Angle?

Remember to look carefully at which angle you are being asked to name.

The reflex angle is the larger angle. 
It is more than 180° but less than 360°

If you choose the smaller angle you might have an Acute Angle, or an Obtuse Angle instead:

Full Rotation

A full rotation is 360 degrees

This is a "full rotation" or "revolution" or "complete turn" or "full circle"

Other ways of saying it:

• "I gave the wheel one complete turn looking for holes"
• "It was spinning at 200 revolutions per minute" (but people usually say "RPM" instead of "revolutions per minute").
• "Doing a 360" means you spin around completely once (spinning around twice is a "720").
• "It completed one cycle", meaning it went around exactly once.
• "She went full circle on liking carrots". So maybe she originally liked carrots, then hated them, now she likes them again.

And a full rotation is also equal to 2π Radians, so here are some equivalent values: