RBSE Solutions for Class 9 Maths Chapter 13 Angles and their Measurement is part of RBSE Solutions for Class 9 Maths. Here we have given Rajasthan Board RBSE Class 9 Maths Solutions Chapter 13 Angles and their Measurement.

Board |
RBSE |

Textbook |
SIERT, Rajasthan |

Class |
Class 9 |

Subject |
Maths |

Chapter |
Chapter 13 |

Chapter Name |
Angles and their Measurement |

Exercise |
Ex 13 |

Number of Questions Solved |
15 |

Category |
RBSE Solutions |

## Rajasthan Board RBSE Class 9 Maths Solutions Chapter 13 Angles and Their Measurement

**Multiple Choice Questions**

Question 1.

The line describing (RBSESolutions.com) an angle of 750°, lies in:

(A) First quadrant

(B) Second quadrant

(C) Third quadrant

(D) Fourth quadrant

Question 2.

The number of radians in angle 30° is:

(A) \(\frac { \pi }{ 3 }\) radian

(B) \(\frac { \pi }{ 4 }\) radian

(C) \(\frac { \pi }{ 6 }\) radian

(D) \(\frac { 3\pi }{ 4 }\) radian

Question 3.

The value of \(\frac { 3\pi }{ 4 }\) in sexagesimal system is:

(A) 75°

(B) 135°

(C) 120°

(D) 220°

Question 4.

The time taken by the minute hand of (RBSESolutions.com) a watch in tracing an angle of \(\frac { \pi }{ 6 }\) radians is:

(A) 10 minutes

(B) 20 minutes

(C) 15 minutes

(D) 5 minutes

Question 5.

The value of the angle, in radian subtended at the centre of the circle of radius 100 metres by an arc of length 25π metres is:

(A) \(\frac { \pi }{ 4 }\)

(B) \(\frac { \pi }{ 3 }\)

(C) \(\frac { \pi }{ 6 }\)

(D) \(\frac { 3\pi }{ 4 }\)

**Answers**

1. A

2. C

3. B

4. D

5. A

Question 6.

In which quadrant does the (RBSESolutions.com) revolving ray lie when it makes the following angles.

(i) 240°

(ii) 425°

(iii) – 580°

(iv) 1280°

(v) – 980°

Solution.

(i) 240° = 2 x right angle + 60°, therefore the position of the revolving ray will be in third quadrant.

(ii) 425° = 4 x right angles + 65°, therefore the position of the revolving ray will be in first quadrant.

(iii) – 580° = – 6 x right angles – 40°, therefore the position of the revolving ray will be in second quadrant.

(iv) 1280° = 14 x right angles + 20°, therefore the position of the revolving ray will be in third quadrant.

(v) – 980° = – 10 x right angles – 80°, therefore the position of the revolving ray will be in second quadrant.

Question 7.

Convert the following angles (RBSESolutions.com) in radians:

(i) 45°

(ii) 120°

(iii) 135°

(iv) 540°

Solution.

Question 8.

Express the following angles (RBSESolutions.com) in sexagesimal system.

(i) \(\frac { \pi }{ 2 }\)

(ii) \(\frac { 2\pi }{ 5 }\)

(iii) \(\frac { 5\pi }{ 6 }\)

(iv) \(\frac { \pi }{ 15 }\)

Solution.

Question 9.

Find the angle in radians subtended at the centre of (RBSESolutions.com) a circle of radius 5 cm by an arc of the circle whose length is 12 cm.

Solution.

We know that:

θ (radian) = \(\frac { arc length }{ radius }\)

We have, radius = 5 cm

and arc length = 12 cm

θ = \(\frac { 12 }{ 5 }\)

Question 10.

How much time the minute hand of a watch will take to describe an angle of \(\frac { 3\pi }{ 2 }\) radians.

Solution.

Time taken by the minute hand of a watch in tracing 4 right angles or an angle equal to 2it radians = 1 hour.

Time taken by the minute hand of a clock in tracing an angle equal to 1 radian = \(\frac { 1 }{ 2\pi }\) hours

Time taken by the minute hand of a clock in tracing an angle equal to \(\frac { 3\pi }{ 2 }\) radians

= \(\frac { 1 }{ 2\pi } \times \frac { 3\pi }{ 2 }\) hours

= \(\frac { 3 }{ 4 }\) hours or 45 minutes 4

Question 11.

How much time the minute hand of a watch will take (RBSESolutions.com) to describe an angle of 120°?

Solution.

We know that:

The minute hand of a watch describes an angle of 4 right angles i.e. 360° in one hour.

the time taken by minute hand to trace an angle of 1° = \(\frac { 1 }{ 360 }\) hours

the time taken by minute hand to trace 120° angle

= \(\frac { 1 }{ 360 }\) x 120

= \(\frac { 1 }{ 3 }\) hours

= \(\frac { 1 }{ 3 }\) x 60 minutes

= 20 minutes.

Question 12.

Find the radius of the circle, if any arc length of 10 cm subtends (RBSESolutions.com) an angle of 60° at the centre of the circle.

Solution.

Question 13.

Find the time if the minute hand of a clock (RBSESolutions.com) has revolved through 30 right angles just after noon.

Solution.

We know that:

The time taken by the minute hand of a clock in tracing 4 right angles is 1 hour.

So, we convert 30 right angles in terms of the multiple of 4 right angles

i.e. 30 right angles

= 7 x (4 right angles) + 2 right angles

= 7 x 1 hr + \(\frac { 1 }{ 2 }\) hr = 7\(\frac { 1 }{ 2 }\) hours

= 7 hours 30 minutes

Hence, time = 7 : 30 p.m.

Question 14.

The angles of a triangle are in (RBSESolutions.com) the ratio of 2 : 3 : 4. Find all the three angles in radians.

Solution.

The A, B and C are angles of any triangle ABC

A : B : C = 2 : 3 : 4

⇒ ∠A = 2x, ∠B = 3x and ∠C = 4x

∠A + ∠B + ∠C = 180° (Angles sum property of a triangle)

⇒ 2x + 3x + 4x = 180°

⇒ 9x = 180°

⇒ x = 20°

Therefore angles (in degrees) are 40°, 60′ and 80°

Question 15.

Convert \(\frac { 3\pi }{ 5 }\) radian into (RBSESolutions.com) sexagesimal system.

Solution.

We hope the given RBSE Solutions for Class 9 Maths Chapter 13 Angles and their Measurement will help you. If you have any query regarding Rajasthan Board RBSE Class 9 Maths Solutions Chapter 13 Angles and their Measurement, drop a comment below and we will get back to you at the earliest.