Chapter 5: Lines and Angles

Q21Written answer

If two supplementary angles are in the ratio 1: 2, then the bigger angle is

(a) 120^o (b) 125^o (c) 110^o (d) 90^o

Show solutionHide solution

Worked solution

Solution:-

(a) 120^o

We know that, when the sum of the measures of two angles is 180^o, then the angles are called supplementary angles.

Let us assume two angles be 1x and 2x.

1x + 2x = 180^o

3x = 180^o

x = 180^o/3

x = 60^o

Then the bigger angle is 2x = 2 × 60^o = 120^o

Q22Written answer

In Fig. 5.19, ∠ROS is a right angle and ∠POR and ∠QOS are in the ratio 1: 5. Then, ∠QOS measures

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 12

(a) 150^o (b) 75^o (c) 45^o (d) 60^o

Show solutionHide solution

Worked solution

Solution:-

(b) 75^o

The sum of all angles about a straight line given in the figure is equal to 180^o.

Given, ∠ROS is a right angle = 90^o

Let us assume ∠POR = x and ∠QOS = 5x.

Then, ∠POR + ∠ROS + ∠QOS = 180^o

x + 90^o+ 5x = 180^o

6x = 180^o – 90^o

6x = 90^o

x = 90^o/6

x = 15^o

So, ∠QOS measures = 5x = 5 × 15^o = 75^o

Q23Written answer

Statements a and b are as given below:

a: If two lines intersect, then the vertically opposite angles are equal.

b: If a transversal intersects two other lines, then the sum of two interior angles on the same side of the transversal is 180^o.

Then

(a) Both a and b are true (b) a is true and b is false

(c) a is false and b is true (d) both a and b are false

Show solutionHide solution

Worked solution

Solution:-

(b) a is true and b is false

Q24Written answer

For Fig. 5.20, statements p and q are given below:

p: a and b are forming a linear pair.

q: a and b are forming a pair of adjacent angles.

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 13

Then,

(a) both p and q are true

(b) p is true and q is false

(c) p is false and q is true

(d) both p and q are false

Show solutionHide solution

Worked solution

Solution:-

(a) both p and q are true

Q25Written answer

In Fig. 5.21, ∠AOC and ∠ BOC form a pair of

(a) vertically opposite angles

(b) complementary angles

(c) alternate interior angles

(d) supplementary angles

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 14

Show solutionHide solution

Worked solution

Solution:-

(d) supplementary angles

Q26Written answer

In Fig. 5.22, the value of a is

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 15

(a) 20^o (b) 15^o

(c) 5^o (d) 10^o

Show solutionHide solution

Worked solution

Solution:-

(d) 10^o

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 16

∠AOF = ∠COD = 90^o [because vertically opposite angles]

Sum of all angles about a straight line given in the figure are equal to 180^o.

Then, ∠BOC + ∠COD + ∠DOE = 180^o

40^o + 90^o + 5a = 180^o

130^o + 5a = 180^o

5a = 180^o – 130^o

5a = 50^o

a = 50/5

a = 10^o

Q27Written answer

In Fig. 5.23, if QP || SR, the value of a is

(a) 40^o (b) 30^o (c) 90^o (d) 80^o

Show solutionHide solution

Worked solution

Solution:-

(c) 90^o

To find out the value of ‘a’, draw a line XY, to cut at ‘a’.

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 18

So, XY || SR

∠XTS = ∠TSR = 30^o … [because interior alternate angles]

∠PQT = ∠QTX = 60^o … [because interior alternate angles]

Then, a = ∠XTS + ∠QTX

= 30^o + 60^o

= 90^o

Q28Written answer

In which of the following figures, a and b are forming a pair of adjacent angles?

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 19

Show solutionHide solution

Worked solution

Solution:-

In figure (d) a and b form a pair of adjacent angles.

Q29Written answer

In a pair of adjacent angles, (i) vertex is always common, (ii) one arm is always common, and (iii) uncommon arms are always opposite rays

Then

(a) All (i), (ii) and (iii) are true

(b) (iii) is false

(c) (i) is false but (ii) and (iii) are true

(d) (ii) is false

Show solutionHide solution

Worked solution

Solution:-

(b) (iii) is false

Two angles are called adjacent angles, if they have a common vertex and a common arm but no common interior points.

Q30Written answer

In Fig. 5.25, lines PQ and ST intersect at O. If ∠POR = 90° and x : y = 3 : 2, then z is equal to

(a) 126^o (b) 144^o (c) 136^o (d) 154^o

NCERT Exemplar Class 7 Maths Solutions Chapter 5 Image 20

Show solutionHide solution

Worked solution

Solution:-

(b) 144^o

The sum of all angles about a straight line given in the figure is equal to 180^o.

PQ is a straight line.

Then, ∠POR + ∠ROT + ∠TOQ = 180^o

Given, x : y = 3 : 2

Let us assume x = 3a, y = 2a

90^o + 3a + 2a = 180^o

90^o + 5a = 180^o

5a = 180^o – 90^o

5a = 90^o

a = 90/5

a = 18^o

So, x = 3a = 3 × 18 = 54^o

y = 2a = 2 × 18 = 36^o

From the figure SOT is a straight line,

Then, z+ y = 180^o

z + 36^o = 180^o

z = 180^o – 36^o

z = 144^o

My Cart

Your Cart 0

Questions