Chapter 13 Angles and their Measurement

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

Multiple Choice Questions

Question 1.
The line describing 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)  radian
(B)  radian
(C)  radian
(D)  radian

Question 3.
The value of  in sexagesimal system is:
(A) 75°
(B) 135°
(C) 120°
(D) 220°

Question 4.
The time taken by the minute hand of a watch in tracing an angle of  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) 
(B) 
(C) 
(D) 

Answers

1. A
2. C
3. B
4. D
5. A

Question 6.
In which quadrant does the 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 in radians:
(i) 45°
(ii) 120°
(iii) 135°
(iv) 540°
Solution.

Question 8.
Express the following angles in sexagesimal system.
(i) 
(ii) 
(iii) 
(iv) 
Solution.

Question 9.
Find the angle in radians subtended at the centre of a circle of radius 5 cm by an arc of the circle whose length is 12 cm.
Solution.
We know that:
θ (radian) = 
We have, radius = 5 cm
and arc length = 12 cm
θ = 

Question 10.
How much time the minute hand of a watch will take to describe an angle of  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 =  hours
Time taken by the minute hand of a clock in tracing an angle equal to  radians
=  hours
=  hours or 45 minutes 4

Question 11.
How much time the minute hand of a watch will take 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° =  hours
the time taken by minute hand to trace 120° angle
=  x 120
=  hours
=  x 60 minutes
= 20 minutes.

Question 12.
Find the radius of the circle, if any arc length of 10 cm subtends an angle of 60° at the centre of the circle.
Solution.

Question 13.
Find the time if the minute hand of a clock 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 +  hr = 7 hours
= 7 hours 30 minutes
Hence, time = 7 : 30 p.m.

Question 14.
The angles of a triangle are in 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  radian into sexagesimal system.
Solution.