An acute angle is an angle that measures between and , or (in radians). Acute angles are always less than .
The word acute comes from Latin, acutus, meaning sharp or pointed. Anytime you see a pointy angle, you have an acute angle.
An acute angle is one of several angles you will encounter in geometry. Acute angles can be any degree greater than and less than .
Here is a tricky example:
Though the acute angle, measuring , is only off the right angle, it is still acute. Mathematics prefers precision, so even an angle cannot be called a right angle; it is an acute angle.
If acute angles are angles that measure between and , what is an angle called if it is exactly? And what if an angle measures more than ?
A right angle is an angle whose measure is exactly or . An angle measuring more than is called an obtuse angle.
Here are examples of what acute, obtuse, and right angles can look like:
|Type of Angle||Angle Pictures|
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 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.
In an acute triangle, all angles are acute. To be an acute triangle, it must have acute angles.
A good example of an acute triangle is an equilateral triangle. The interior angles of all triangles must sum to , so in an equilateral triangle, where all three angles have the same measure, we know that each interior angle is an acute angle.
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).
Acute angles are everywhere around you.
The easiest way to make or draw an acute angle is to write a capital letter A. This will create three acute angles.
After working your way through this lesson and video, you have learned:
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