# S.L. Loney Measurement of Angles Solutions (Chapter 1)

SL Loney Plane Trigonometry Solutions for Chapter 1 ‘Measurement of Angles’ is a complete resource to learn and clear your concepts regarding the various systems to measure angles. Measurement and conversion angles among various systems are some of the crucial chapters you must finish before getting into complex mathematics such as trigonometry. SL Loney Trigonometry solutions for Measurement of Angles would clear your concepts related to angles and also sets the foundation for advanced math topics, which can be really vital for preparation for JEE (mains and advanced), NEET and other competitive examinations.

SL Loney Plane Trigonometry Measurement of Angles solutions comprises 4 exercises and 84 questions. To solve these questions, it first requires you to go through the book and learn more about angles and various angle systems (Centesimal & Sexagesimal angle systems), conversion between the angle systems, circular measure, magnitude of radian and theorems. The SL Loney solutions by Instasolv are structured curatively to give you a clear perspective of the topics covered in the chapter.

Instasolv provides you with Complete Solutions to SL Loney Measurement of Angles which are well written and designed by our subject-matter experts in such a way to give a maximum understanding of the topics. The solutions also contain required formulas, keynotes along with the required diagrammatic representation for the problem. All this will certainly improve your understanding of JEE and NEET like exams.

## Important topics for SL Loney Plane Trigonometry solution chapter 1: Measurement of Angles

Measurement of angles is an essential topic as you need to deal with these angles in upcoming chapters including trigonometric formulas and equations. Angles are really helpful in determining other properties either height or distance between objects (using trigonometry) by knowing the other values. The crucial topics covered across SL Loney Plane Trigonometry Solutions for Measurement of Angles are as follows:

**Angles:**

When two rays intersect in a plane, the figure formed at the vertex (intersecting point of two rays) is called an angle.

**Measurement of angles**:

In geometry, angels are mentioned in right angles. Though there are many conductive approaches and systems to measure the same.

**Sexagesimal system**

- In the Sexagesimal system, the right angle is divided further into Degrees, Minutes and Seconds.
- Right-angle consists of 90 Degrees, A Degree comprises 60 Minutes and a Minute consists of 60 seconds. A Degree, Minute and Second can be represented by using the symbols 1°, 1’ and 1” respectively.

**Centesimal system**

- The Centesimal system is similar to the Sexagesimal system as in this system, a right angle is divided into 100 parts called Grades, the Grades are further divided into 100 minutes, where each minute consists of 100 seconds.
- In the Centesimal system, a Grade, a minute and a second are denoted as 1
^{g}, 1‵ and 1‶ respectively.

**Conversion within the angle systems:**

Since here we have used many systems to measure angles, we need to convert them from one system to another. As we know the Right-angle measures the same as 90 Degrees in the Sexagesimal system and 100 Grades in the Centesimal system.

Therefore, 90°=100^{ g}

^{ }1°=10^{ g}/9

1^{ g} =9 °/10

**Angles of any size**:

In this section, you will learn more about determining the angles in terms of Right angle. In simpler words, any angle can be easily represented in terms of Right angle. For example, 380° comprises one revolution while it has traced 4 Right angles and 20°. The topic also includes 1 example and 31 solved examples to better understanding.

**Circular Measure:**

In this section, you will come across another measuring system, called Circular measure. The angle is measured in Radian (denoted by °).

**Theorems**:

These are some of the essential theorems related to Circular measure which you must cover. The following topic has 2 examples and 4 solved examples. Some of the theorems are:

- The ratio of the circumference of a circle to its diameter is always constant for any given circle and is equal to ‘Pi’ (π).
- The value of Pi is equal to 22/7 (3.14159).
**The magnitude of a Radian:**

In this section, you will come across Radian.

1 Radian = (2/ π) x a right angle = 180°/ π

Angles can be described in terms of Radians as follows:

180° = 2 Right angles = π Radians

360° = 4 Right angles = 2π Radians

Similarly, if an angle makes n revolutions it can be described as 2n π Radians. The conversions can be tricky for newbies, but thanks to SL Loney Plane Trigonometry chapter 1: Measurement of Angles, which has 4 examples along with 28 solved examples.

**The Theorem of Radian:**

The theorem states that the ratio of the length of arc subtended by the angle to the radius of the circle is equal to the Radians.

### Exercise Discussion for SL Loney Plane Trigonometry Solutions Chapter 1: Measurement of Angles

SL Loney Plane Trigonometry Measurement of Angles comprises 84 questions across four exercises. Every exercise covers questions from different topics. After solving them you will be able to know about various angle systems and conversion between them. Let’s see them in detail.

**Exercise I**

In the first exercise, you need to express a given angle in terms of right-angle. You will also face questions which require conversion of a given angle into the centesimal system. These questions can be solved easily by applying the required formulas.

**Exercise II**

In this exercise, you will need to deal with questions related to the circular measure. Like you will be given a radius or diameter of the circle and then you need to calculate various parameters (such as circumference, speed in case of wheel and other details provided).

**Exercise III**

In the third exercise, you need to convert the given angle (in degrees, grades) to angle (in radians) and vice versa. You will also find problems like angles given in A.P. (arithmetic progression) and find respective angles. Lastly, you need to find angles of various polygons (in radians and degrees).

**Exercise IV**

In the final exercise, you will be given 20 problems to solve. The problems are based on the theorem of radians and can be easily solved by applying the required formula (angle in radians = length of arc/radius)

## Why Use SL Loney Plane Trigonometry Solutions Chapter 1: Measurement of Angles by Instasolv?

- Maths can be really boring and complex if you are learning in a misguided way. Complete Solutions to SL Loney Solutions Measurement of Angles is a perfect remedy for you if you are also an aspirant for higher education.
- At Instasolv, we are determined for your success and therefore prepare solutions for every difficulty you face while studying.
- The solutions add up every required detail regarding the topic along with formulas and diagrams which empowers you to conceptualize the topic in an enhanced way.
- Solutions by Instasolv are easily available online for free of cost and are prepared in sync with the latest IIT JEE Maths syllabus.