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# Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 1 - Angle and its Measurement [Latest edition]

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#### Chapters ## Chapter 1: Angle and its Measurement

Exercise 1.1Exercise 1.2Miscellaneous Exercise 1
Exercise 1.1 [Pages 8 - 9]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 1 Angle and its Measurement Exercise 1.1 [Pages 8 - 9]

Exercise 1.1 | Q 1. (A) (i) | Page 8

Determine which of the following pairs of angles are co-terminal 210°, – 150°

Exercise 1.1 | Q 1. (A) (ii) | Page 8

Determine which of the following pair of angles is co-terminal.

360°, −30°

Exercise 1.1 | Q 1. (A) (iii) | Page 8

Determine which of the following pair of angles is co-terminal.

−180°, 540°

Exercise 1.1 | Q 1. (A) (iv) | Page 8

Determine which of the following pair of angles is co-terminal.

−405°, 675°

Exercise 1.1 | Q 1. (A) (v) | Page 8

Determine which of the following pair of angles is co-terminal.

860°, 580°

Exercise 1.1 | Q 1. (A) (vi) | Page 8

Determine which of the following pair of angles is co-terminal.

900°, −900°

Exercise 1.1 | Q 1. (B) (i) | Page 8

Draw the angle of the following measure and determine their quadrant.

–140°

Exercise 1.1 | Q 1. (B) (ii) | Page 8

Draw the angle of the following measure and determine their quadrant.

250°

Exercise 1.1 | Q 1. (B) (iii) | Page 8

Draw the angle of the following measure and determine their quadrant.

420°

Exercise 1.1 | Q 1. (B) (iv) | Page 8

Draw the angle of the following measure and determine their quadrant.

750°

Exercise 1.1 | Q 1. (B) (v) | Page 8

Draw the angle of the following measure and determine their quadrant.

945°

Exercise 1.1 | Q 1. (B) (vi) | Page 8

Draw the angle of the following measure and determine their quadrant.

1120°

Exercise 1.1 | Q 1. (B) (vii) | Page 8

Draw the angle of the following measure and determine their quadrant.

–80°

Exercise 1.1 | Q 1. (B) (viii) | Page 8

Draw the angle of the following measure and determine their quadrant.

–330°

Exercise 1.1 | Q 1. (B) (ix) | Page 8

Draw the angle of the following measure and determine their quadrant.

–500°

Exercise 1.1 | Q 1. (B) (x) | Page 8

Draw the angle of the following measure and determine their quadrant.

–820°

Exercise 1.1 | Q 2. (i) | Page 8

Convert the following angle into radian:

85°

Exercise 1.1 | Q 2. (ii) | Page 8

Convert the following angle into radian:

250°

Exercise 1.1 | Q 2. (iii) | Page 8

Convert the following angle into radian:

−132°

Exercise 1.1 | Q 2. (iv) | Page 8

Convert the following angles into radian:

65°30′

Exercise 1.1 | Q 2. (v) | Page 8

Convert the following angles into radian:

75°30′

Exercise 1.1 | Q 2. (vi) | Page 8

Convert the following angles into radian:

40°48′

Exercise 1.1 | Q 3. (i) | Page 8

Convert the following angles in degree.

(7pi^"c")/12

Exercise 1.1 | Q 3. (ii) | Page 8

Convert the following angles in degree:

(-5pi^"c")/3

Exercise 1.1 | Q 3. (iii) | Page 8

Convert the following angles in degree:

5c

Exercise 1.1 | Q 3. (iv) | Page 8

Convert the following angles in degree:

(11pi^"c")/18

Exercise 1.1 | Q 3. (v) | Page 8

Convert the following angles in degree:

((-1)/4)^"c"

Exercise 1.1 | Q 4. (i) | Page 8

Express the following angle in degree, minute and second:

(183.7)°

Exercise 1.1 | Q 4. (ii) | Page 8

Express the following angle in degree, minute and second:

(245.33)°

Exercise 1.1 | Q 3. (iii) | Page 8

Express the following angle in degree, minute and second:

(1/5)^"c"

Exercise 1.1 | Q 5 | Page 8

In ∆ABC, if m∠A = (7pi^"c")/36, m∠B = 120°, find m∠C in degree and radian.

Exercise 1.1 | Q 6 | Page 8

Two angles of a triangle are (5pi^"c")/9 and (5pi^"c")/18. Find the degree and radian measures of third angle.

Exercise 1.1 | Q 7 | Page 8

In a right angled triangle, the acute angles are in the ratio 4:5. Find the angles of the triangle in degrees and radians.

Exercise 1.1 | Q 8 | Page 8

The sum of two angles is 5πc and their difference is 60°. Find their measures in degrees.

Exercise 1.1 | Q 9 | Page 8

The measures of the angles of a triangle are in the ratio 3:7:8. Find their measures in degrees and radians.

Exercise 1.1 | Q 10 | Page 9

The measures of the angles of a triangle are in A.P. and the greatest is 5 times the smallest (least). Find the angles in degrees and radian.

Exercise 1.1 | Q 11 | Page 9

In a cyclic quadrilateral two adjacent angles are 40° and pi^"c"/3. Find the angles of the quadrilateral in degrees.

Exercise 1.1 | Q 12 | Page 9

One angle of a quadrilateral has measure (2pi^"c")/5 and the measures of other three angles are in the ratio 2 : 3 : 4. Find their measures in degree and radian.

Exercise 1.1 | Q 13. (i) | Page 9

Find the degree and radian measure of exterior and interior angle of a regular pentagon

Exercise 1.1 | Q 13. (ii) | Page 9

Find the degree and radian measure of exterior and interior angle of a regular hexagon

Exercise 1.1 | Q 13. (iii) | Page 9

Find the degree and radian measure of exterior and interior angle of a regular Septagon

Exercise 1.1 | Q 13. (iv) | Page 9

Find the degree and radian measure of exterior and interior angle of a regular Octagon

Exercise 1.1 | Q 14. (i) | Page 9

Find the angle between hour-hand and minute-hand in a clock at ten past eleven

Exercise 1.1 | Q 14. (ii) | Page 9

Find the angle between hour-hand and minute-hand in a clock at twenty past seven

Exercise 1.1 | Q 14. (iii) | Page 9

Find the angle between hour-hand and minute-hand in a clock at thirty five past one

Exercise 1.1 | Q 14. (iv) | Page 9

Find the angle between hour-hand and minute-hand in a clock at quarter to six

Exercise 1.1 | Q 14. (v) | Page 9

Find the angle between hour-hand and minute-hand in a clock at 2 : 20

Exercise 1.1 | Q 14.(vi) | Page 9

Find the angle between hour-hand and minute-hand in a clock at 10 : 10

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Exercise 1.2 [Page 11]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 1 Angle and its Measurement Exercise 1.2 [Page 11]

Exercise 1.2 | Q 1 | Page 11

Find the length of an arc of a circle which subtends an angle of 108° at the centre, if the radius of the circle is 15 cm.

Exercise 1.2 | Q 2 | Page 11

The radius of a circle is 9 cm. Find the length of an arc of this circle which cuts off a chord of length, equal to length of radius.

Exercise 1.2 | Q 3 | Page 11

Find the angle in degree subtended at the centre of a circle by an arc whose length is 15 cm, if the radius of the circle is 25 cm.

Exercise 1.2 | Q 4 | Page 11

A pendulum of length 14 cm oscillates through an angle of 18°. Find the length of its path.

Exercise 1.2 | Q 5 | Page 11

Two arcs of the same lengths subtend angles of 60° and 75° at the centres of two circles. What is the ratio of radii of two circles?

Exercise 1.2 | Q 6 | Page 11

The area of a circle is 25π sq.cm. Find the length of its arc subtending an angle of 144° at the centre. Also find the area of the corresponding sector.

Exercise 1.2 | Q 7 | Page 11

OAB is a sector of the circle having centre at O and radius 12 cm. If m∠AOB = 45°, find the difference between the area of sector OAB and sector AOB.

Exercise 1.2 | Q 8 | Page 11

OPQ is the sector of a circle having centre at O and radius 15 cm. If m∠POQ = 30°, find the area enclosed by arc PQ and chord PQ.

Exercise 1.2 | Q 9 | Page 11

The perimeter of a sector of the circle of area 25π sq.cm is 20 cm. Find the area of sector.

Exercise 1.2 | Q 10 | Page 11

The perimeter of the sector of the circle of area 64π sq.cm is 56 cm. Find the area of the sector.

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Miscellaneous Exercise 1 [Pages 12 - 13]

### Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board Chapter 1 Angle and its Measurement Miscellaneous Exercise 1 [Pages 12 - 13]

Miscellaneous Exercise 1 | Q 1. I (01) | Page 12

Select the correct option from the given alternatives :

((22pi)/15)^"c" is equal to

• 246°

• 264°

• 224°

• 426°

Miscellaneous Exercise 1 | Q 1. I (02) | Page 12

Select the correct option from the given alternatives :

156° is equal to

• ((17pi)/5)^"c"

• ((13pi)/15)^"c"

• ((11pi)/15)^"c"

• ((7pi)/15)^"c"

Miscellaneous Exercise 1 | Q 1. I (03) | Page 12

Select the correct option from the given alternatives :

A horse is tied to a post by a rope. If the horse moves along a circular path, always keeping the rope tight and describes 88 metres when it traces the angle of 72° at the centre, then the length of the rope is

• 70 m

• 55 m

• 40 m

• 35 m

Miscellaneous Exercise 1 | Q 1. I (04) | Page 12

Select the correct option from the given alternatives :

A pendulum of 14cms long oscillates through an angle of 12°, then the angle of the path described by its extrimities is

• (13pi)/14

• (14pi)/13

• (15pi)/14

• (14pi)/15

Miscellaneous Exercise 1 | Q 1. I (05) | Page 12

Select the correct option from the given alternatives.

Angle between hand’s of a clock when it shows the time 9.45 is

• (7.5)°

• (12.5)°

• (17.5)°

• (22.5)°

Miscellaneous Exercise 1 | Q 1. I (06) | Page 12

Select the correct option from the given alternatives :

20 metres of wire is available for fencing off a flower-bed in the form of a circular sector of radius 5 metres, then the maximum area (in sq. m.) of the flower-bed is

• 15

• 20

• 25

• 30

Miscellaneous Exercise 1 | Q 1. I (07) | Page 12

Select the correct option from the given alternatives :

If the angles of a triangle are in the ratio 1 : 2 : 3, then the smallest angle in radian is

• pi/3

• pi/6

• pi/2

• pi/9

Miscellaneous Exercise 1 | Q 1. I (08) | Page 12

Select the correct option from the given alternatives :

A semicircle is divided into two sectors whose angles are in the ratio 4:5. Find the ratio of their areas?

• 5:1

• 4:5

• 5:4

• 3:4

Miscellaneous Exercise 1 | Q 1. I (09) | Page 12

Select the correct option from the given alternatives :

Find the measure of the angle between hour-hand and the minute hand of a clock at twenty minutes past two.

• 50°

• 60°

• 54°

• 65°

Miscellaneous Exercise 1 | Q 1. I (10) | Page 12

Select the correct option from the given alternatives :

The central angle of a sector of circle of area 9π sq.cm is 60°, the perimeter of the sector is

• π

• 3 + π

• 6 + π

• 6

Miscellaneous Exercise 1 | Q 2. II (01) | Page 12

Answer the following :

Find the number of sides of a regular polygon, if each of its interior angle is (3pi^"c")/4.

Miscellaneous Exercise 1 | Q 2. II (02) | Page 12

Answer the following :

Two circles each of radius 7 cm, intersect each other. The distance between their centres is 7sqrt(2) cm. Find the area common to both the circles.

Miscellaneous Exercise 1 | Q 2. II (03) | Page 12

Answer the following :

ΔPQR is an equilateral triangle with side 18 cm. A circle is drawn on segment QR as diameter. Find the length of the arc of this circle within the triangle.

Miscellaneous Exercise 1 | Q 2. II (04) | Page 12

Answer the following :

Find the radius of the circle in which central angle of 60° intercepts an arc of length 37.4 cm.

Miscellaneous Exercise 1 | Q 2. II (05) | Page 13

Answer the following :

A wire of length 10 cm is bent so as to form an arc of a circle of radius 4 cm. What is the angle subtended at the centre in degree ?

Miscellaneous Exercise 1 | Q 2. II (06) | Page 13

Answer the following :

If two arcs of the same length in two circles subtend angles 65° and 110° at the centre. Find the ratio of their radii.

Miscellaneous Exercise 1 | Q 2. II (07) | Page 13

Answer the following :

The area of a circle is 81π sq.cm. Find the length of the arc subtending an angle of 300° at the centre and also the area of corresponding sector.

Miscellaneous Exercise 1 | Q 2. II (08) | Page 13

Answer the following :

Show that the minute-hand of clock gains 5°30' on the hour-hand in one minute.

Miscellaneous Exercise 1 | Q 2. II (09) | Page 13

Answer the following :

A train is running on a circular track of radius 1 km at the rate of 36 km per hour. Find the angle, to the nearest minute, through which it will turn in 30 seconds.

Miscellaneous Exercise 1 | Q 2. II (10) | Page 13

Answer the following :

In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.

Miscellaneous Exercise 1 | Q 2. II (11) | Page 13

Answer the following :

The angles of a quadrilateral are in A.P. and the greatest angle is double the least. Find angles of the quadrilateral in radian.

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## Chapter 1: Angle and its Measurement

Exercise 1.1Exercise 1.2Miscellaneous Exercise 1 ## Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 1 - Angle and its Measurement

Balbharati solutions for Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 1 (Angle and its Measurement) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the Maharashtra State Board Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Mathematics and Statistics 1 (Arts and Science) 11th Standard Maharashtra State Board chapter 1 Angle and its Measurement are Directed Angle, Angles of Different Measurements, Angles in Standard Position, Measures of Angles, Area of a Sector of a Circle, Length of an Arc of a Circle.

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