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# RD Sharma Class 11 Chapter 4 Solutions (Measurement of Angles)

RD Sharma Solutions, for Class 11 Chapter 4 Measurement of Angles are prepared to help you get a strong foundation of the basic concept of mathematics. This can help you beat the exams and further will support you determine the academic and career path you may follow in future. In this chapter, we will see the science of measuring angles, the system for measuring those angles, the relationship between those systems, and few conversions.

This chapter consists of one exercise 4.1 including 20 practical questions and 8 multiple-choice questions. In these short and detailed Questions, you will need to find out radian measures, degree measures, magnitude, angles in radians. Some complex questions will ask you to express the angles in radians and degrees, determine the side of polygons, find the length of an arc, a ratio of radii etc.

InstaSolv has identified the most frequent doubts of students and the most demanded questions in examination thus we have come up with the detailed illustration of solving each problem and explaining all the concepts and formulae in brief. We have used an ideal algorithm technique to reach the solution of any given problem. This will help you understand the complexity of the chapter more quickly, ultimately creating a strong grip over the sub-topics and will also improve your analyzing skill.

## Topics covered in RD Sharma for Class 11 Chapter 4 Measurement Of Angles

Trigonometry is a branch of Science. It deals with measuring Angles. The whole Trigonometry revolves around the same.

Definition of Angle

When we measure the rotation from the initial side to the terminal side, that amount of rotation is known as Angle.

Sexagesimal System

This system is also commonly called as English system. The principal unit of this system is a degree (°).

When we divide the Right angle equally in 90 parts. That part is called a Degree.

When This 1° is again divided equally into 60 parts. Each part is called a minute denoted by 1’.

One minute is divided into 60 equal parts. Each part is called a second.

So, it can go like;

60 seconds (or 60”) = 1 minute (or 1’)

60 minutes (or 60’) = 1 degree (or 1°)

90 minutes (or 90°) = 1 right Angle

Centesimal System

Another important system of measurement of angles is the centesimal system. The principal unit of this system is grade denoted by ‘g’.

One right angle is divided into 100 equal parts called grades.

Each grade is further subdivided into 100 minutes and each minute into 100 seconds.

In mathematical form, this can be represented as:

One right angle = 100g

1g = 100 minutes

1 minute = 100 seconds

Circular System

We use ‘Radian‘ as a unit of measurement in this system. It is based on the relationship between circumference and radius of the circle.

A Radian is measured when an angle subtends at the Centre of the circle by an arc, where the length of an arc is equal to the radius of the circle.

One Radian (1c) = arc length of magnitude ‘r’/ Radius of circle ‘r’

(where the ratio is independent and the radian is constant)

## Relationship between Sexagesimal System and Centesimal System

One right angle = 90 degrees (or 90°) and

One right angle = 100g

Thus we can say that  90° = 100g

So finally, we have 1° = (10/9) g or 1g = (9/10) °

## D/90= G/100=2C/π

Basic Formulae Used in Chapter

Degrees = Radians x 180/ π

Bullet Highlights for Chapter 4 Measurement of Angles

1.     In the first 10 questions, you will learn to find degree, radians, express the angles, length of an arc, determine the angle, find the number of sides of a polygon. You will practice more Questions of finding angles of radians in exercise 4.1.
2.     Multiple Questions are mainly formulae based where you will find the right solution with the help of formulas like calculating radius, the angle subtended by arc, angular velocity and relation between degree, grade and radian.
3.     The questions are aligned with the flow of all the topics which will prove easy to learn and solve.