Angles are formed whenever 2 lines intersect, or meet.
An acute angle is an angle that measures less than 90°. It is smaller than a right angle but greater than a 0° angle.
Example:
∠CAT is less than a right angle, so it is acute.
The arc inside the angle indicates the space occupied by the angle.
Look at the angles below. Which is an acute angle?
∠MOP is acute
Finding Acute Angles in the Real World
Did you know that angles are all around us? Think about everyday objects—many of them form acute angles without us even realizing it! Unlike obtuse angles, which are wide and open, or straight angles, which form a straight line, acute angles have a small, narrow opening.
Here are some fun examples:
- A slice of pizza – The tip of the slice forms an acute angle.
- An ice cream cone – The bottom of the cone creates a sharp, pointed angle.
- A pair of scissors (slightly opened) – The blades form an acute angle when not fully open.
Measuring an Acute Angle with a Protractor
Angle measurement is based on the concept of the fraction of a circle occupied by the angle.
A full rotation inside a circle has a total of 360°.
Angles are composed from very small units called degrees. There are a total of 360 1° units in a circle. A 1° angle is very tiny!
The angle ∠XYZ is formed by two rays, one extending from point Y through X and another extending from point Y through Z. The common endpoint, point Y, is called the vertex of the angle.
In this case, ∠XYZ measures 10°, which makes it an acute angle because it is less than 90°.
You can measure angles using a tool called a protractor.
To measure with a protractor, line one ray of the angle up with the straight bottom of the protractor.
∠HIJ measures 50°.
It is an acute angle.
Notice that if ray IH kept going, it would pass right through the number 50.
Practice Problems
Which is an acute angle?
Which of the following angles is an acute angle?
Which object most likely forms an acute angle?
