What is an Angle?
Two rays or lines meeting at a common point lead to the formation of an angle. An angle is represented using the ‘\( \angle\)’ symbol.
In math, angles are measured in two different units. They are:
- Degrees (°)
- Radians (in terms of \( \pi\) )
We use a protractor to measure angles. The protractor measures angles in degrees (°).
Parts of an Angle
An angle consists of a vertex and two sides. The sides and vertex of an angle can be described as:
- The vertex of an angle is the point at which two lines (or rays) meet.
- Angle sides are the two rays or lines that meet to form the angle.
The angle ABC formed as shown in the image can be written as ‘∠ABC’, or ∠CBA, or simply as ∠B.
AB and BC are the sides of ∠ABC, and B is the vertex of ∠ABC.
How Do We Measure an Angle?
The following steps can be used to measure angles with a protractor:
Step 1: Place the center of the protractor at the vertex of an angle.
Step 2: Align the baseline of the protractor with one side of the angle.
Step 3: Another side of the angle on the protractor indicates the measure of the angle in degrees. Measure anticlockwise if you have chosen the right baseline, or clockwise if you have chosen the left base line of the protractor.
\( \angle~AMC\) = 40°
What is an Acute Angle?
An acute angle is an angle that measures less than a right angle. In mathematical terms, an angle measuring less than 90 degrees is called an acute angle.
Examples of acute angles include 85°, 5°, 71°, 22° and so on.
An acute angle of 45° can be sketched as shown in the image.
Properties of an Acute Angle
The properties of acute angles are mentioned below:
- A right angle can be divided into two or more acute angles.
- All equilateral triangles are made up of acute angles.
- Any angle that is 90 degrees or greater is not considered to be an acute angle.
- Any triangle has a minimum of two acute angles.
Real-Life Examples of Acute Angle
A few real-life examples of acute angles are given below:
- The English letter ‘V’ has an acute angle.
- The hands of a clock form an acute angle when the time is 12:10.
- A pizza slice forms an acute angle.
- Few exercise postures also form acute angles.
Solved Acute Angle Examples
Name the type of angle. If
A. \( x\) = 30°
B. \( x\) = 55°
C. \( x\) = 90°
D. \( x\) = 165°
Solution:
A. Here \( x\) = 30°
30 < 90
So, the angle in option A is an acute angle.
B. Here \( x\) = 55°
55 < 90
So, the angle in option B is an acute angle.
C. Here \( x\)= 90°
90 = 90
So, the angle in option C is a right angle.
D. \( x\) = 165°
165 > 90
So, the angle in option D is an obtuse angle.
Example 2:
Which of the following letters has an acute angle?
A) T
B) O
C) V
D) G
Solution:
Letter ‘V’ contains an acute angle.
So, option C is correct.
Example 3:
Write five examples of an acute angle in degrees.
Solution:
The five examples of an acute angle in degrees are 30°, 4°, 65°, 87°, and 79°.
Example 4:
What type of angle is formed between the minute and hour hand of a watch at 2:00 o’clock?
Solution:
From the above figure, the angle formed between minutes and hours is less than 90 degrees. So, it is an acute angle.
A 35-degree angle is an acute angle since 35 degrees is less than 90 degrees.
Yes, any angle less than 90 degrees is called an acute angle. Therefore, a 0-degree angle is an acute angle.
Yes, the angles of equilateral triangles are acute because each angle of an equilateral triangles is 60 degrees, which is less than 90. Therefore, they are acute angles.
There are two acute angles in a right-angled triangle.
On the basis of the measure of an angle, angles can be classified into four types:
- Acute angle
- Right angle
- Obtuse angle
- Straight angle