What Is an Acute Angle?

In real life, there are many examples of acute angles

An acute angle is an angle with a measurement between 0° and 90°, or with less than 90° radians. It's the smallest of six different types of angles.

There's an easy way to remember that an acute angle is small: think of it as "a cute angle," perhaps visualizing a cute child playing an acute angle in a play about geometry.

Note that an angle measuring exactly 90° is not an acute angle. Instead, it's a right angle.

Acute Angle: One of Six Angle Types in Math

When you think of angles, you should think of them as part of the radius of a circle, which is 360° in total. An acute angle makes up less than one-quarter of that circle's radius—again, less than 90°.

There are five other types of angles, all making up greater percentages of that circle's radius:

  • Right angles are 90° exactly, or one-quarter exactly of the circle's 360° radius.
  • Obtuse angles fall between 90° and 180°, or between one-quarter and one-half of the circle's radius. Note that they do not include angles that are exactly 90° or 180°.
  • Straight angles are exactly 180°, or exactly one-half of the circle's radius. They look like a straight line.
  • Reflex angles are between 180° and 360°, or more than one-half of the circle's radius. They do not include angles that are exactly 180° or 360°.
  • Full angles are exactly 360°, or the full circle's radius. Like straight angles, they look like a straight line, but they mean something completely different.

    Looking for Examples of Acute Angles in Real Life

    You'll find plenty of examples of acute angles in real life.

    For example, an open safety pin forms an acute angle, as does a set of barbecue tongs, a skateboard ramp, the blades on an open pair of scissors and the "Live Well and Prosper" hand sign from the television and movie series Star Trek.

    The nose on a paper airplane forms an acute angle, as does a sharp point on a number two yellow pencil, most Y-shaped street intersections, an analog clock showing the time is one o'clock or two o'clock, and even the top of a Christmas tree.

    And of course, a piece of pizza generally forms an acute angle (as long as you're not eating more than your share of the pie).