Concise Mathematics Class 6 ICSE Solutions for Chapter 24 - Angles (With their Types)

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Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 24 Angles (With their Types) part-1

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Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 24 Angles (With their Types) part-3Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 24 Angles (With their Types) part-3

Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 24 Angles (With their Types) part-4Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 24 Angles (With their Types) part-4

Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 24 Angles (With their Types) part-5Selina Concise Mathematics Class 6 ICSE Solutions for Chapter 24 Angles (With their Types) part-5

The concept of angles comes into existence when two lines intersect each other. Studies of Angles are a part of our day-to-day life. For example, you are seeing the bulb of your room at some angle, a man standing on a flat road makes an angle with the nearby building, etc. Also, When you open a book the two pages are at a certain angle.

The angles have a very important role in architecture. And it makes their study and classification more important. In this article, you are going to learn about the angles and their classification. In this article you'll read about these topics which are given below here:

•  Angles

• Interior of Angle

• Exterior of Angle

• Degree

• Types of Angles

• Classification of Angles according to their position

• Classification the based on the sum of angles

• Classification of the angles on the base of their rotation

Angle

• An angle is made when two lines or planes intersect each other. The angles and their classification has plenty of applications, especially in architecture and trigonometry.

• The angle is the rotation with which one of the sides should be turned to coincide with the other line. 

1. Interior of Angle 

The interior of the angle is the area between two lines or planes where the measurement of the angle is minimum.

2. Exterior of Angle 

The exterior of the angle is the area between two lines or planes where the measurement of the angle is maximum.

Degree 

• The degree is the unit of measurement of angles.

• If two lines have a 0° angle then its meaning is that both are parallel. The maximum value of an angle in one rotation can be 360 °. A straight line has an angle of 180° at any of the points on the line.

• A common tool that is used to measure the angle is Protector. It has a mark of 0° to 180°.

Types of Angles 

1. Complete Angles 

Complete angle is the angle of 360°.

2. Right Angle 

A right angle is the angle of 90°. It makes a quarter of rotation I.e. 1/4th of the circle.

3. Straight Angle 

A straight angle is defined as the angle of 180°. It makes a half revolution.

4. Acute Angles 

An acute angle is defined as an angle that is less than 90°.

5. Obtuse Angle 

An obtuse angle is the angle of an angle that is more than 90° but less than 180°.

6. Reflex Angle 

A reflex angle is defined as an angle that is more than 180°.

Classification of Angles according to Their Position

We can divide angles into further categories based on their position 

1. Adjacent Angles

• The two angles are adjacent if they are following any of these properties

• If They will have a common vertex.

• If They have one common arm.

       2. Vertically Opposite Angles

The angles on the opposite side of the point of intersection are called vertically opposite angles.

        3. Alternate Interior Angles

When two parallel lines are intersected by a transversal, then eight angles are formed there. The pair of interior angles which are between parallel lines and transversal are called interior angles.

        4. Congruent Angles 

The angles which are the same in measurement are called congruent angles.

Classification The Based on The Sum of Angles 

Angles are divided into two categories based on sum of these angles. These are :

• Complementary Angles

• Supplementary Angles

1. Complementary Angles

1. The complementary work is derived from the Latin word " completum". The meaning of "completum" is complete.

2. Complementary angles are defined as the angles whose sum is 90°. Each of the angles of this type is called a complement of another.

2. Supplementary Angles 

1. The pair of angles which add up to give 180° are called supplementary angles. Each angle of this pair is called the supplement of the other.

Angles have Some Distinct Properties which are as Follows 

• The sum of angles on a straight line will always be exactly 180°. For example, if you have any straight line and two and three lines intersect with it. Where the sum of angles on one side of a straight line will be exactly 180°.

• The angles are vertically opposite due to the intersection of two lines being equal.

• Alternate Interior Angles are always equal.

• The angles which are co-interior to each other add up to give the sum of 180°

• Corresponding angles are always equal.

Classification on The Base of Rotation

We can also classify angles based on their rotation. On the base of rotation Angles are divided into two categories.

• Positive Angle

• Negative Angle

1. Positive Angle: The angles which are measured by the anticlockwise rotation, are called positive angles.

2. Negative Angle: The angles which are measured by the clockwise rotation, are called positive angles.

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