An acute angle is an angle that measures less than 90 degrees.
A right angle is an angle that measures exactly 90 degrees.
An obtuse angle is an angle that measures more than 90 degrees but less than 180 degrees.
A straight angle is an angle that measures exactly 180 degrees.
Acute angles are named by their vertex points, which are the letters used to label the angle. For example, the acute angles shown in the diagram below are labeled A, B, and C.
Angle A is between sides a and b.
Angle B is between sides b and c.
Angle C is between sides c and a.
The acute angles shown in the diagram above are labeled A, B, and C.
Angle A is between sides a and b.
Angle B is between sides b and c.
Angle C is between sides c and a.
Acute angles have the following properties:
The measure of an acute angle is always less than 90 degrees.
Acute angles are always less than right angles.
Acute angles are always less than obtuse angles.
Acute angles are complementary to obtuse angles. That is, the sum of the measures of an acute angle and an obtuse angle is equal to 180 degrees.
The formula for finding the measure of an acute angle is m=90-x where x is the measure of the acute angle.
Examples of Acute Angles
Here are some examples of acute angles:
Angle ABC is an acute angle.
Angle BAC is an acute angle.
Angle CAB is an acute angle.
All of these angles have a measure that is less than 90 degrees. Notice that in each case, the vertex point is labeled with the letter B and the sides are labeled with the letters A and C.
The following diagram shows another example of an acute angle. This time, the angle is between two lines rather than two line segments. The angle shown in this diagram is also an acute angle because its measure is less than 90 degrees.
When we talk about angles, we usually think of them as being between two line segments. However, it is important to remember that an angle can also be formed by two lines. In the diagram above, the angle is formed by the lines l and m. The vertex point of the angle is labeled with the letter V.
Acute angles can also be found in everyday life. The following are some examples of acute angles that you might encounter:
The angle formed by the handle of a screwdriver and the shaft of the screwdriver
The angle formed by the blade of a knife and the handle of the knife
The angle between your thumb and index finger when you make an “OK” sign
The angle between your arm and your body when you flex your arm
The angle between your leg and your body when you sit in a chair with your legs crossed
As you can see, acute angles are all around us!
