NCERT Solutions Maths Ch-5 Lines and Angles for Class 7th

NCERT Solutions of class 7th maths Chapter 5 Lines and Angles Exercise 5.1

Q1. Find the complement of each of the following angles:

Solution:
(i) Complement of 20° = 90° – 20° = 70°
(ii) Complement of 63° = 90° – 63° = 27°
(iii) Complement of 57° = 90° – 57° = 33°

2. Find the supplement of each of the following angles:

Solution:
(i) Supplement of 105° = 180° – 105° = 75°
(ii) Supplement of 87° = 180° – 87° = 93°
(iii) Supplement of 154° = 180° – 154° = 26°

3. Identify which of the following pairs of angles are complementary and which are supplementary.

(i) 65^o, 115^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 65^o + 115^o

= 180^o

If the sum of two angle measures is 180^o, then the two angles are said to be supplementary.

∴These angles are supplementary angles.

(ii) 63^o, 27^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 63^o + 27^o

= 90^o

If the sum of two angle measures is 90^o, then the two angles are said to be complementary.

∴These angles are complementary angles.

(iii) 112^o, 68^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 112^o + 68^o

= 180^o

If the sum of two angle measures is 180^o, then the two angles are said to be supplementary.

∴These angles are supplementary angles.

(iv) 130^o, 50^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 130^o + 50^o

= 180^o

If the sum of two angle measures is 180^o, then the two angles are said to be supplementary.

∴These angles are supplementary angles.

(v) 45^o, 45^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 45^o + 45^o

= 90^o

If the sum of two angle measures is 90^o, then the two angles are said to be complementary.

∴These angles are complementary angles.

(vi) 80^o, 10^o

Solution:-

We have to find the sum of given angles to identify whether the angles are complementary or supplementary.

Then,

= 80^o + 10^o

= 90^o

If the sum of two angle measures is 90^o, then the two angles are said to be complementary.

∴These angles are complementary angles.

4. Find the angles which is equal to its complement.

Solution:-

Let the measure of the required angle be x^o.

We know that, sum of measures of complementary angle pair is 90^o.

Then,

= x + x = 90^o

= 2x = 90^o

= x = 90/2

= x = 45^o

Hence, the required angle measures is 45^o.

5. Find the angles which is equal to its supplement.

Solution:-

Let the measure of the required angle be x^o.

We know that, sum of measures of supplementary angle pair is 180^o.

Then,

= x + x = 180^o

= 2x = 180^o

= x = 180/2

= x = 90^o

Hence, the required angle measures is 90^o.

6. In the given figure, ∠1 and ∠2 are supplementary angles. If ∠1 is decreased, what changes should take place in ∠2 so that both angles still remain supplementary.

Solution:-

From the question, it is given that,

∠1 and ∠2 are supplementary angles.

If ∠1 is decreased, then ∠2 must be increased by the same value. Hence, this angle pair remains supplementary.

7. Can two angles be supplementary if both of them are:

(i). Acute?

Solution:-

No. If two angles are acute, means less than 90^o, the two angles cannot be supplementary. Because, their sum will be always less than 90^o.

(ii). Obtuse?

Solution:-

No. If two angles are obtuse, means more than 90^o, the two angles cannot be supplementary. Because, their sum will be always more than 180^o.

(iii). Right?

Solution:-

Yes. If two angles are right, means both measures 90^o, then two angles can form a supplementary pair.

∴90^o + 90^o = 180

8. An angle is greater than 45^o. Is its complementary angle greater than 45^o or equal to 45^o or less than 45^o?

Solution:-

Let us assume the complementary angles be p and q,

We know that, sum of measures of complementary angle pair is 90^o.

Then,

= p + q = 90^o

It is given in the question that p > 45^o

Adding q on both the sides,

= p + q > 45^o + q

= 90^o > 45^o + q

= 90^o – 45^o > q

= q < 45^o

Hence, its complementary angle is less than 45^o.

9. In the adjoining figure:

i) Is ∠1 adjacent to ∠2?

Solution:-

By observing the figure we came to conclude that,

Yes, as ∠1 and ∠2 having a common vertex i.e. O and a common arm OC.

Their non-common arms OA and OE are on both the side of common arm.

(ii) Is ∠AOC adjacent to ∠AOE?

Solution:-

By observing the figure, we came to conclude that,

No, since they are having a common vertex O and common arm OA.

But, they have no non-common arms on both the side of the common arm.

(iii) Do ∠COE and ∠EOD form a linear pair?

Solution:-

By observing the figure, we came to conclude that,

Yes, as ∠COE and ∠EOD having a common vertex i.e. O and a common arm OE.

Their non-common arms OC and OD are on both the side of common arm.

(iv) Are ∠BOD and ∠DOA supplementary?

Solution:-

By observing the figure, we came to conclude that,

Yes, as ∠BOD and ∠DOA having a common vertex i.e. O and a common arm OE.

Their non-common arms OA and OB are opposite to each other.

(v) Is ∠1 vertically opposite to ∠4?

Solution:-

Yes, ∠1 and ∠2 are formed by the intersection of two straight lines AB and CD.

(vi) What is the vertically opposite angle of ∠5?

Solution:-

∠COB is the vertically opposite angle of ∠5. Because these two angles are formed by the intersection of two straight lines AB and CD.

10. Indicate which pairs of angles are:

(i) Vertically opposite angles.

Solution:-

By observing the figure we can say that,

∠1 and ∠4, ∠5 and ∠2 + ∠3 are vertically opposite angles. Because these two angles are formed by the intersection of two straight lines.

(ii) Linear pairs.

Solution:-

By observing the figure we can say that,

∠1 and ∠5, ∠5 and ∠4 as these are having a common vertex and also having non common arms opposite to each other.

11. In the following figure, is ∠1 adjacent to ∠2? Give reasons.

Solution:-

∠1 and ∠2 are not adjacent angles. Because, they are not lie on the same vertex.

12. Find the values of the angles x, y, and z in each of the following:

Solution:- (i)

∠x = 55^o, because vertically opposite angles.

∠x + ∠y = 180^o … [∵ linear pair]

= 55^o + ∠y = 180^o

= ∠y = 180^o – 55^o

= ∠y = 125^o

Then, ∠y = ∠z … [∵ vertically opposite angles]

∴ ∠z = 125^o

(ii)

Solution:-

∠z = 40^o, because vertically opposite angles.

∠y + ∠z = 180^o … [∵ linear pair]

= ∠y + 40^o = 180^o

= ∠y = 180^o – 40^o

= ∠y = 140^o

Then, 40 + ∠x + 25 = 180^o … [∵angles on straight line]

65 + ∠x = 180^o

∠x = 180^o – 65

∴ ∠x = 115^o

13. Fill in the blanks:

Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is ______ .
(ii) If two angles are supplementary, then the sum of their measures is ______ .
(iii) Two angles forming a linear pair are ______ .
(iv) If two adjacent angles are supplementary, they form a ______ .
(v) If two lines intersect at a point, then the vertically opposite angles are always ______ .
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are ______ .
Solution:
(i) 90°
(ii) 180°
(iii) Supplementary
(iv) Linear pair
(v) Equal
(vi) Obtuse angle

14. In the adjoining figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles

Solution:-

∠AOD and ∠BOC are obtuse vertically opposite angles in the given figure.

(ii) Adjacent complementary angles

Solution:-

∠EOA and ∠AOB are adjacent complementary angles in the given figure.

(iii) Equal supplementary angles

Solution:-

∠EOB and EOD are the equal supplementary angles in the given figure.

(iv) Unequal supplementary angles

Solution:-

∠EOA and ∠EOC are the unequal supplementary angles in the given figure.

(v) Adjacent angles that do not form a linear pair

Solution:-

∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD are the adjacent angles that do not form a linear pair in the given figure.