Angles are the foundation of geometry in mathematics and without proper knowledge about them, it is impossible to solve different geometrical questions. There are different types of angles in geometry and acute angle forms the major part. Through this guide, you will better understand the concept of different types of angles and what actually acute angles are in mathematics.
What are angles in geometry?
Whenever two straight line segments intersect at a point, then an angle is formed. The angle in geometry is represented by the symbol ‘∠’. The two straight lines forming the angle after joining are referred to as arms of the angle and the point where these two arms intersect is referred to as vertex. The measurement unit of the angle is degree or radian.
What are different types of angles in geometry?
Based on the direction of rotation, it can be said that there are two types of angles, one is positive angles and the other one is negative angles.
- Positive Angle: A positive angle is an angle that goes in counterclockwise.
- Negative Angle: A negative angle is an angle that goes in a clockwise direction.
The following are the different types of angles:
- Acute Angle: It is the angle less than 90 degrees.
- Right Angle: It is the angle equal to 9 degrees.
- Obtuse Angle: It is the angle greater than 90 degrees and less than 180 degrees.
- Straight Angle: It is the angle equal to 180 degrees.
- Reflex Angle: It is the angle greater than 180 degrees but less than 360 degrees.
- Full Angle: It is the angle equal to 360 degrees.
Based on these angles and lines, some more types of angles are classified such as complementary angles, vertical angles, supplementary angles, adjacent angles, alternate interior and alternate exterior angles, and many other angles.
What are acute angles?
As it is already discussed, an angle is formed when two straight rays intersect at the common point known as the vertex. An acute angle is the most important type of angle. And an angle can be called an acute angle when the measure of the formed angle is less than 90 degrees. In other words, it can be said that the measure of the angle less than the right angle is known as the acute angle. Hence, the measure of acute angle ranges from 0 degrees to less than 90 degrees such as 23, 55
, 67
, 88
Mentioning the properties of acute angles:
- Properties of acute-angled triangles:
Whenever all three interior angles of the triangle will be less than 90 degrees, then the particular triangle will be referred to as an acute angle triangle. Therefore, the equilateral triangle having all interior angles equal to 60 degrees can be also called an acute angle triangle.
- Properties of acute-angled parallelogram:
A parallelogram is a figure with four sides, in which two pairs of sides are opposite and equal. In a parallelogram, the opposite angles are always equal (congruent) to each other. And it is a known fact that there are two obtuse and two acute angles in the parallelogram. Therefore, it can be concluded that the measurement of acute angle and obtuse angles should be equal.
Bottom Line
Now that you know what are different types of angles and acute angles, practice the questions related to these concepts so that you can build strong mathematical skills. In case you have doubts related to any other mathematical concepts, you can join Cuemath. It is an online educational platform that provides after-school math programs to the students so that they can understand the complicated math concepts according to their convenience.
