## 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:

Question 2.

In which of the following figures, are ∠AOB and ∠AOC adjacent angles? Give, in each case, reason for your answer.

Solution:

Question 3.

In the given figure, B AC is a straight line.

Find : (i) x (ii) ∠AOB (iii) ∠BOC

Solution:

Question 4.

Find yin the given figure.

Solution:

Question 5.

In the given figure, find ∠PQR.

Solution:

Question 6.

In the given figure. p° = q° = r°, find each.

Solution:

Question 7.

In the given figure, if x = 2y, find x and y

Solution:

Question 8.

In the adjoining figure, if b° = a° + c°, find b.

Solution:

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.

Solution:

Question 10.

Write the complement of:

Solution:

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:

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:

Question 13.

Are the following pairs of angles supplementary?

Solution:

Question 14.

If 3x + 18° and 2x + 25° are supplementary, find the value of x.

Solution:

Question 15.

If two complementary angles are in the ratio 1:5, find them.

Solution:

Question 16.

If two supplementary’ angles are in the ratio 2 : 7, find them.

Solution:

Question 17.

Three angles which add upto 180° are in the ratio 2:3:7. Find them.

Solution:

Question 18.

20% of an angle is the supplement of 60°. Find the angle.

Solution:

Question 19.

10% of x° is the complement of 40% of 2x°. Find x

Solution:

Question 20.

Use the adjacent figure, to find angle x and its supplement.

Solution:

Question 21.

Find k in each of the given figures.

Solution:

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.

Solution:

Question 23.

In the given figure, find ∠AOB and ∠BOC.

Solution:

Question 24.

Find each angle shown in the diagram.

Solution:

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.

Solution:

### 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

Solution:

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

Solution:

Question 3.

In the given figures, the arrows indicate parallel lines. State which angles are equal. Give reasons.

Solution:

Question 4.

In the given figure, find the measure of the unknown angles :

Solution:

Question 5.

Which pair of the dotted line, segments, in the following figures, are parallel. Give reason:

Solution:

Question 6.

In the given figures, the directed lines are parallel to each other. Find the unknown angles.

Solution:

Question 7.

Find x. y and p is the given figures

Solution:

Question 8.

Find x in the following cases :

Solution:

### 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:

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:

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:

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:

Question 5.

Construct an angle of 75° and then bisect it.

Solution:

Question 6.

Draw a line segment of length 6 .4 cm. Draw its perpendicular bisector.

Solution:

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:

Question 8.

In each case, given below, draw a line through point P and parallel to AB :

Solution: