Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles

Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles)

Selina Publishers Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles (Including Construction of angles)

Lines and Angles Exercise 14A – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
State, true or false :
(i) A line segment 4 cm long can have only 2000 points in it.
(ii) A ray has one end point and a line segment has two end-points.
(iii) A line segment is the shortest distance between any two given points.
(iv) An infinite number of straight lines can be drawn through a given point.
(v) Write the number of end points in
(a) a line segment AB (b) arayAB
(c) a lineAB
(vi) Out of \(\overleftrightarrow { AB }\) , \(\overrightarrow { AB }\) , \(\overleftarrow { AB }\) and \(\overline { AB }\) , which one has a fixed length?
(vii) How many rays can be drawn through a fixed point O?
(viii) How many lines can be drawn through three
(a) collinear points?
(b) non-collinear points?
(ix) Is 40° the complement of 60°?
(x) Is 45° the supplement of 45°?
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 1

Question 2.
In which of the following figures, are ∠AOB and ∠AOC adjacent angles? Give, in each case, reason for your answer.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q2
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q2.1

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 2

Question 3.
In the given figure, B AC is a straight line.
Find : (i) x (ii) ∠AOB (iii) ∠BOC
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q3
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 3

Question 4.
Find yin the given figure.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q4
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 4

Question 5.
In the given figure, find ∠PQR.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q5
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 5

Question 6.
In the given figure. p° = q° = r°, find each.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q6
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 6

Question 7.
In the given figure, if x = 2y, find x and y
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q7
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 7

Question 8.
In the adjoining figure, if b° = a° + c°, find b.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q8
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 8

Question 9.
In the given figure, AB is perpendicular to BC at B.
Find : (i) the value of x.
(ii) the complement of angle x.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q9
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 9

Question 10.
Write the complement of:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q10
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q10.1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 10

Question 11.
Write the supplement of:
(i) 100°
(ii) 0°
(iii) x°
(iv) (x + 35)°
(v) (90 +a + b)° f
(vi) (110 – x – 2y)°
(vii) \(\frac { 1 }{ 5 }\) of a right angle
(viii) 80° 49′ 25″
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 11
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 12

Question 12.
Are the following pairs of angles complementary ?
(i) 10° and 80°
(ii) 37° 28′ and 52° 33′
(iii) (x+ 16)°and(74-x)°
(iv) 54° and \(\frac { 2 }{ 5 }\) of a right angle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 13

Question 13.
Are the following pairs of angles supplementary?
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q13
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 14

Question 14.
If 3x + 18° and 2x + 25° are supplementary, find the value of x.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 15

Question 15.
If two complementary angles are in the ratio 1:5, find them.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 16

Question 16.
If two supplementary’ angles are in the ratio 2 : 7, find them.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 17

Question 17.
Three angles which add upto 180° are in the ratio 2:3:7. Find them.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 18

Question 18.
20% of an angle is the supplement of 60°. Find the angle.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 19

Question 19.
10% of x° is the complement of 40% of 2x°. Find x
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 20

Question 20.
Use the adjacent figure, to find angle x and its supplement.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q20
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 21

Question 21.
Find k in each of the given figures.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q21
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q22

Question 22.
In the given figure, lines PQ, MN and RS intersect at O. If x : y = 1 : 2 and z = 90°, find ∠ROM and ∠POR.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q22

Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 23

Question 23.
In the given figure, find ∠AOB and ∠BOC.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q23
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 24

Question 24.
Find each angle shown in the diagram.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q24
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 25

Question 25.
AB, CD and EF are three lines intersecting at the same point.
(i) Find x, if y = 45° and z = 90°.
(ii) Find a, if x = 3a, y = 5x and r = 6x.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A Q25
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 26
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14A 27

Lines and Angles Exercise 14B – Selina Concise Mathematics Class 7 ICSE Solutions

In questions 1 and 2, given below, identify the given pairs of angles as corresponding angles, interior alternate angles, exterior alternate angles, adjacent angles, vertically opposite angles or allied angles :
Question 1.
(i) ∠3 and ∠6
(ii) ∠2 and ∠4
(iii) ∠3 and ∠7
(iv) ∠2 and ∠7
(v) ∠4 and∠6
(vi) ∠1 and ∠8
(vii) ∠1 and ∠5
(viii) ∠1 and ∠4
(ix) ∠5 and ∠7
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 28

Question 2.
(i) ∠1 and ∠4
(ii) ∠4 and ∠7
(iii) ∠10 and ∠12
(iv) ∠7 and ∠13
(v) ∠6 and ∠8
(vi) ∠11 and ∠8
(vii) ∠7 and ∠9
(viii) ∠4 and ∠5
(ix) ∠4 and ∠6
(x) ∠6 and ∠7
(xi) ∠2 and ∠13
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q2
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 29

Question 3.
In the given figures, the arrows indicate parallel lines. State which angles are equal. Give reasons.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q3
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 30

Question 4.
In the given figure, find the measure of the unknown angles :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q4
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 31

Question 5.
Which pair of the dotted line, segments, in the following figures, are parallel. Give reason:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q5
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q5.1
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 32
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 33

Question 6.
In the given figures, the directed lines are parallel to each other. Find the unknown angles.
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q6
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q6.2
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q6.3
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 34
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 35
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 36
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 37
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 38
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 39
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 40
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 41>

Question 7.
Find x. y and p is the given figures
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q7
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 42
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 43

Question 8.
Find x in the following cases :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q8
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q8.1
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B Q8.2
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 44
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 45
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14B 46

Lines and Angles Exercise 14C – Selina Concise Mathematics Class 7 ICSE Solutions

Question 1.
Using ruler and compasses, construct the following angles :
(i)30°
(ii)15°
(iii) 75°
(iv) 180°
(v) 165°
(vi) 22.5°
(vii) 37.5°
(viii) 67.5°
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 47
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 48
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 49
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 50
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 51
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 52
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 53
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 54

Question 2.
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses only. Measure each 1 angle so obtained and check whether the angles obtained on bisecting ∠ABC are equal or not.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 55

Question 3.
Draw a line segment PQ = 6 cm. Mark a point A in PQ so that AP = 2 cm. At point A, construct angle QAR = 60°.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 56

Question 4.
Draw a line segment AB = 8 cm. Mark a point P in AB so that AP = 5 cm. At P, construct angle APQ = 30°.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 57

Question 5.
Construct an angle of 75° and then bisect it.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 58

Question 6.
Draw a line segment of length 6 .4 cm. Draw its perpendicular bisector.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 59

Question 7.
Draw a line segment AB = 5.8 cm. Mark a point P in AB such that PB = 3.6 cm. At P, draw perpendicular to AB.
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 60

Question 8.
In each case, given below, draw a line through point P and parallel to AB :
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C Q8
Solution:
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 61
Selina Concise Mathematics Class 7 ICSE Solutions Chapter 14 Lines and Angles Ex 14C 62

Selina Concise Mathematics Class 7 ICSE Solutions

Leave a Comment