Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles (With their Types)

Selina Publishers Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles (With their Types)

Angles Exercise 24A – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
For each angle given below, write the name of the vertex, the names of the arms and the name of the angle.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 1

Question 2.
Name the points :
(i) in the interior of the angle PQR,
(ii) in the exterior of the angle PQR.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q2
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 2

Question 3.
In the given figure, figure out the number of angles formed within the arms OA and OE.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q3
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 3

Question 4.
Add :
(i) 29° 16′ 23″ and 8° 27′ 12″
(ii) 9° 45’56” and 73° 8′ 15″
(m) 56° 38′ and 27° 42’30”
(iv) 47° and 61° 17’4″
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 4

Question 5.
In the figure, given below name :
(i) three pairs of adjacent angles.
(ii) two acute angles,
(iii) two obtuse angles
(iv) two reflex angles.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q5
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 5

Question 6.
In the given figure ; PQR is a straight line. If :
(i) ∠SQR = 75° ; find ∠PQS.
(ii) ∠PQS = 110°; find ∠RQS
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q6
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 6

Question 7.
In the given figure ; AOC-is a straight line. If angle AOB = 50°, angle AOE = 90° and angle COD = 25° ; find the measure of :
(i) angle BOC
(ii) angle EOD
(iii) obtuse angle BOD
(iv) reflex angle BOD
(v) reflex angle COE.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q7
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 7

Question 8.
In the given figure if :
(i) a = 130° ; find b.
(ii) b = 200 ; find a.
(iii) a = 5/3 right angle, find b
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q8
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 8

Question 9.
In the given diagram, ABC is a straight line.
(i) If x = 53°, find y.
(ii) If y =1\(\frac { 1 }{ 2 }\) right angles ; find x.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q9
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 9

Question 10.
In the given figure, AOB is a straight line. Find the value ofx and also answer each of the following :
(i) ∠AOP = ……..
(ii) ∠BOP = ……..
(iii) which angle is obtuse ?
(iv) which angle is acute ?
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q10
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 10

Question 11.
In the given figure, PQR is a straight line. Find x. Then complete the following:
(i) ∠AQB = ……..
(ii) ∠BQP = ……..
(iii) ∠AQR = …….
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q11
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 11

Question 12.
In the given figure, lines AB and CD intersect at point O.
(i) Find the value of ∠a.
(ii) Name all the pairs of vertically opposite angles.
(iii) Name all the pairs of adjacent angles.
(iv) Name all the reflex angles formed and write the measure of each.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q12
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 12

Question 13.
In the given figure :
(i) If ∠AOB = 45°, ∠BOC = 30° and ∠AOD= 110°;
find : angles COD and BOD.
(ii) If ∠BOC = ∠DOC = 34° and ∠AOD = 120° ;
find : angle AOB and angle AOC.
(iii) If ∠AOB = ∠BOC = ∠COD = 38°
find : reflex angle AOC and reflex angle AOD.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A Q13
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24A 13

Angles Exercise 24B – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Write the complement angle of :
(i) 45°
(ii) x°
(iii) (x – 10)°
(iv) 20° + y°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 14

Question 2.
Write the supplement angle of :
(i) 49°
(ii) 111°
(iii) (x – 30)°
(iv) 20° + y°
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 15

Question 3.
Write the complement angle of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B Q3
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B Q3.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 16

Question 4.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B Q4

Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 17

Question 5.
Find the angle :
(i) that is equal to its complement ?
(ii) that is equal to its supplement ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 18

Question 6.
Two complementary angles are in the ratio 7 : 8. Find the angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 19

Question 7.
Two supplementary angles are in the ratio 7 : 11. Find the angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 20

Question 8.
The measures of two complementary angles are (2x – 7)° and (x + 4)°. Find x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 21

Question 9.
The measures of two supplementary angles are (3x + 15)° and (2x + 5)°. Find x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 22

Question 10.
For an angle x°, find :
(i) the complementary angle
(ii) the supplementary angle
(iii) the value of x° if its supplementary angle is three times its complementary angle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Ex 24B 23

Angles Revision Exercise – Selina Concise Mathematics Class 6 ICSE Solutions

Question 1.
Explain what do you understand by :
(i) Adjacent angles ?
(ii) Complementary angles ?
(iii) Supplementary angles ?
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 24

Question 2.
Find the value of ‘x’ for each of the following figures :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex Q2
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex Q2.1
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 25
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 26

Question 3.
Find the number of degrees in an angle that is (i) \(\frac { 3 }{ 5 }\) of a right angle (ii) 0.2 times of a straight line angle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 27

Question 4.
In the given figure; AB, CD and EF are straight lines. Name the pair of angles forming :
(i) straight line angles.
(ii) vertically opposite angles.
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex Q4
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 28

Question 5.
Find the complement of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex Q5
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 29

Question 6.
Find the supplement of :
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex Q6
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 30

Question 7.
Two complementary angles are in the ratio 8 : 7. Find the angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 31

Question 8.
Two supplementary angles are in the ratio 7 : 5. Find the angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 32

Question 9.
Two supplementary angles are (5x – 82°) and (4x + 73°). Find the value of x.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 33

Question 10.
Find the angle formed by the arms of a clock at:
(i) 3 O’clock
(ii) 6 O’clock
(iii) 9 O’clock
(iv) 12 O’clock
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 34

Question 11.
For an angle y°, find :
(i) its supplementary angle.
(ii) its complementary angle.
(iii) the value of y° if its supplement is four times its complement.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 35

Question 12.
Use the adjoining figure to find :
(i) ∠BOD
(ii) ∠AOC
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 36

Question 13.
Two adjacent angles forming a linear pair are in the ratio 7:5, find the angles.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 37

Question 14.
Find the angle that is three times its complementary angle.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 38

Question 15.
An angle is one-thirds of a straight line angle ; find :
(i) the angle
(ii) the complement and the supplement of the angle obtained above.
Solution:
Selina Concise Mathematics Class 6 ICSE Solutions Chapter 24 Angles Revision Ex 39

Selina Concise Mathematics Class 6 ICSE Solutions