## Acute Angle Definition

An acute angle is an angle that measures between $0°$ and $90°$, or $\frac{\pi }{2}$ (in radians). Acute angles are always less than $90°$.

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

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.

• 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 ($180°$).

## 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 $\frac{\pi }{2}$. 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
Obtuse angle
Right angle

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.

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.

## 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:

You use angles in everyday life. Even the words you see in print are full of acute angles. The letters are all formed with 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.

## 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.

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