RS Aggarwal Class 6 Solutions Chapter-13 Angles and Their Measurement

We have provided step by step solutions for all exercise questions given in the pdf of Class 6 RS Aggarwal Chapter-13 Angles and Their Measurement. All the Exercise questions with solutions in Chapter-13 Angles and Their Measurement are given below:

• Exercise (Ex 13A) 13.1

• Exercise (Ex 13B) 13.2

• Exercise (Ex 13C) 13.3

• Exercise (Ex 13D) 13.4

Let us look into the important concepts studied in RS Aggarwal Class 6 Chapter 13.

• Angle concept

• Parts of angles

• Why is the angle used?

• Rotation of an angle

• Angle measurement

Angle Concept

An angle is a figure created by two rays in Euclidean geometry, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. In the plane which contains the rays, angles created by two rays lie.

Angles are normally represented by Greek letters like α, β, ω etc.

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Parts of Angles

There are 3 main parts in an angle as given below.

• Vertex - The corner points of the angle are known as the vertex. It is the point at which two rays come together.

• Arms - Both sides of the angle are joined at a common endpoint. It is also known as the reference line. Measurements are carried out using this line as the reference line.

• Angle - Measured between two arms.

Why is the Angle Used?

An angle is often used to mark a rotation measurement. This calculation is the ratio of a circular arc's length to its radius. In the case of a geometric angle, the vertex is centered on the arc and the sides are delimited. The arc is centered at the center of the rotation, in the case of a rotation, and delimited by every other point and its image by the rotation.

Angle Types

In geometry, there are primarily six types of angles. With their properties, the names of all angles are as follows:

• Acute Angle: It is between 0 and 90°.

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• Obtuse Angle: It ranges from 90° to 180°.

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• Right Angle: An angle equal to exactly 90°.

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• Straight Angle: The angle that is exactly equal to 180 °. 

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• Reflex Angle: An angle greater than 180 ° and less than 360 °.

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• Full Angle: Rotation equivalent to 360°.

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Rotation of an Angle

In the coordination plane, angles of rotation are formed between the positive x-axis (initial side) and a ray (terminal side).

Based on the rotation of angles further, it can be classified into two types:

• Positive Angle - This is an angle determined in the anti-clockwise direction.

• Negative Angle - This is an angle determined in the clockwise direction.

There are infinitely many ways to define an angle of rotation. A positive or negative angle of rotation or by making several full circle rotations by 360 ° will explain it.

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Basic Concept Oriented Problems on Angles

1) The angle 89° is called __________.

Ans: By definition of acute angle 89° lies between 0° and 90°. Therefore we can say 89° is called an acute angle.

2) The angle 234° is called _________.

Ans: Angle 234° is greater than 180 ° and less than 360 °. Therefore this is called the Reflex angle.

3) The angle 98° is called __________.

Ans: It is obtuse, as 98 ° is greater than 90 °, but less than 180 °.

Angle Measurement

One of the most important principles of geometry is the theory of angle. The principles of equality, quantities, and angle differences are important and used in geometry, but the trigonometry topic is focused on angle measurement.

For angles, there are two widely used units of measurement.

• Degrees are the more familiar unit of measurement. A circle is divided into equal degrees of 360, such that 90° is a right angle.

• Radians are the other common measurement for angles.

Degrees may be divided further into minutes and seconds, but the division is not as universal as it used to be. Each degree is split into sixty equal sections called minutes. Furthermore, each minute is divided into 60 equal sections called seconds.

For example, 2 degrees 5 minutes 30 seconds can be represented as  2° 5'30''.

The angle division of degrees into minutes and seconds is identical to the angle division of hours into minutes and seconds.

Consider the unit circle (radius=1), the center of which is the vertex of the angle in question, for radian calculation. And the angle cuts off the circle's arc, and the length of that arc is the angle's radial measurement. Between measuring degrees and measuring radians, it is simple to convert. The whole circle's diameter is 2π, so it follows that 360° is equivalent to 2π radians.

From this, we can write 1° = π180 radians

Also, 1 radian = 180π degrees.

Tips to Prepare for Exams Using Angles and Their Measurement Class 6

• Always carry a set of geometrical instruments to answer any questions from the Angles and measurements chapter.

• Understand the basic concepts of angles and practice how to measure the angles using a protractor before exams.

• Be thorough with the types of angles and their measurements as in exams a small assumption of a wrong angle will lead to a completely wrong answer.

Conclusion

The Angles and their Measurement Class 6 is one of the most important chapters for class 6 students as it helps students to understand the basic concepts of Angles and their Measurement and their application in our everyday life. These RS Aggarwal Solutions Class 6 Math Chapter 13 are prepared by the Vedantu experts according to the NCERT curriculum. These solutions are crafted neatly in a detailed step-by-step manner to make students understand the concepts clearly without any doubts. The free PDF of Math RS Aggarwal Class 6 Chapter 13 is available on the Vedantu platform which can be accessed freely by the students.