Acute Angle Definition

An acute angle is an angle that measures between 0° and 90°, or π2 (in radians). Acute angles are always less than 90°.

Acute Angle Definition

The word acute comes from Latin, acutus, meaning sharp or pointed. Anytime you see a pointy angle, you have an acute angle.

Table Of Contents

  1. Acute Angle Definition
  2. What Is An Acute Angle?
  3. Acute, Obtuse, and Right Angles
  4. Acute Angle Shapes
  5. Acute Angle Examples
  6. Make An Acute Angle

What Is An Acute Angle?

An acute angle is one of several angles you will encounter in geometry. Acute angles can be any degree greater than 0° and less than 90°.

Here is a tricky example:

Acute Angle Degree Example

Though the acute angle, measuring 89°, is only 1° off the right angle, it is still acute. Mathematics prefers precision, so even an 89.9° angle cannot be called a right angle; it is an acute angle.

Facts About Acute Angles

  • One acute angle will always measure between 0° and 90°.
  • Two acute angles can sum to be either greater than, less than, or equal to a right angle.
  • Two acute angles can be complementary angles (adding to 90°).
  • Two acute angles alone cannot sum to make a straight angle (180°).

Facts About Acute Angles

Acute, Obtuse, and Right Angles

If acute angles are angles that measure between 0° and 90°, what is an angle called if it is 90° exactly? And what if an angle measures more than 90°?

A right angle is an angle whose measure is exactly 90° or π2. An angle measuring more than 90° is called an obtuse angle.

Here are examples of what acute, obtuse, and right angles can look like:

Acute, Obtuse, and Right Angles
Type of Angle Angle Pictures
Acute angle Acute Angle Picture
Obtuse angle Obtuse Angle Picture
Right angle Right Angle Picture

Acute, Obtuse, and Right Angles Examples

In addition to these angles, there are more angles to know, such as reflex angle, straight angle, and full angles. Learn more about the different types of angles you will encounter in geometry.

Acute Angle Shapes

Acute angles are constantly popping up in geometry. You can find acute angles as exterior angles in shapes with five or more vertices like pentagons and octagons.

You can also find acute angles as interior angles in rhomboids and triangles.

Acute Angle Shapes

Consider the isosceles and equilateral triangles, which depend on two and three acute angles for their construction.

How Many Acute Angles Are In An Acute Triangle?

In an acute triangle, all angles are acute. To be an acute triangle, it must have 3 acute angles.

A good example of an acute triangle is an equilateral triangle. The interior angles of all triangles must sum to 180°, so in an equilateral triangle, where all three angles have the same measure, we know that each interior angle is an acute 60° angle.

How Many Acute Angles Are In An Acute Triangle

Acute Angle Examples

Examples of acute angles in real life are all around you. Acute angle things are sharp; they come to a sharp point. The sharp edge of a knife is an acute angle. A sharpened wood pencil has an acute end, and so does a pair of scissors:

Acute Angles In Everyday Life Items

You use angles in everyday life. Even the words you see in print are full of acute angles. The letters A, K, M, N, R, V, W, X, Y, Z are all formed with acute angles.

Letters That Have Acute Angles

An example of an acute angle in the house are the hands of an analog clock, but only at four different hours (10, 11, 1, and 2 o'clock).

At 12 o'clock, the hands make a zero degree angle.

Acute angles are everywhere around you.

How To Make An Acute Angle

The easiest way to make or draw an acute angle is to write a capital letter A. This will create three acute angles.

Next Lesson:

Angle Pairs

What you learned:

After working your way through this lesson and video, you have learned:

  • The definition of an acute angle
  • The degree of acute angles
  • What shapes that are made with acute angles
  • Several examples of acute angles
Instructor: Malcolm M.
Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.
Tutors online
Ashburn, VA

20+ Math Tutors are available to help

Get better grades with tutoring from top-rated professional tutors. 1-to-1 tailored lessons, flexible scheduling. Get help fast. Want to see the math tutors near you?