NCERT Solutions for Class 7 Mathematics Chapter 5 - Lines and Angles Exercise 5.1

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Please find the detailed Solutions for class 7th Maths Chapter 5 – Lines and Angles Exercise 5.1 Solutions, you can check all the solutions from here chapter wise

NCERT Class 7th Mathematics Solutions – Detailed Chapter Wise

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

Sol: The sum of measures of complementary angles is 90

(i) 20°

20° + x = 90°

x = 90° – 20° = 70°

Complementary angle of 20° = 70°

(ii) 63°

63° + x = 90°

x = 90° – 63° = 27°

Complementary angle of 63° = 27°

(iii) 57°

57° + x = 90°

x = 90° – 57° = 33°

Complementary angle of 57° = 33°

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

Sol: The sum of measures of supplementary angles is 180°
(i) 105°

105° + x = 180°

x = 180° – 105° = 75°

Supplementary angle of 105° = 75°

(i) 87°

87° + x = 180°

x = 180° – 87° = 93°

Supplementary angle of 87° = 93°

(i) 154°

154° + x = 180°

x = 180° – 154° = 26°

Supplementary angle of 154° = 26°

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

Sol: We know that the sum of measures of supplementary angles is 180° and the sum of measures of complementary angles is 90° .

(i) 65° + 115° = 180°

So, these angles are supplementary.

(ii) 63º, 27º

63° + 27° = 90°

Therefore, these angles are complementary.

(iii) 112º, 68º

112° + 68° =180°

Therefore, these angles are supplementary

(iv) 130º, 50º

130° + 50° = 180°

Therefore, these angles are supplementary.

(v) 45º, 45º

45° +45° = 90°

Therefore, these angles are complementary.

(vi) 80º, 10º

80° +10° = 90°

Therefore, these angles are complementary.

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

Sol: We know that the sum of measures complementary angles is 90°.

Let the angles be x.

Then its complement will also be x because both are equal.

x+x = 90°

2x = 90°

2x/2 = 90°/2

x = 45°

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

Sol: We know that the sum of measures of supplementary angles is 180°.

Let the angles be x, then its supplementary angle will also be x.

Now, x+x = 180°

2x = 180°

x = 90°

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 the angles still remain
supplementary.

Ans: ∠1 and ∠2 are supplementary, so their sum will be equal to 180°

Now if ∠1 is decreased then we will have to increase the ∠2 with same measure to keep the sum equal to 180°.

7. Can two angles be supplementary if both of them are:
(i) acute? (ii) obtuse? (iii) right?

Ans: The sum of measures of supplementary angles is 180°

(i) No, the measure of acute angle is less than 90°. The sum of two acute angles will be less than 180°. Therefore two acute angles cannot be supplementary.

(ii) No, the measure of obtuse angle is greater than 90°. The sum of two obtuse angles will be more than 180°. Therefore two obtuse angles cannot be supplementary.

(iii) Yes, the measure of right angle is equal to 90°. The sum of two right angles is equal to 180°.

Therefore two right angles are supplementary.

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

Ans: If a angle is greater than 45° then its complementary angle will be less than 45°.

9. In the adjoining figure:

(i) Is ∠1 adjacent to ∠2?

Ans: Yes, ∠1 is adjacent to ∠2 because they have common vertex O and common arm OC and their non-common arms lies on either sides of common arm.

(ii) Is ∠AOC adjacent to ∠AOE?

Ans: No, ∠AOC is not adjacent to ∠AOE, because they have common vertex O and common arm OC but their non-common arms lies on same sides of common arm.

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

Ans: Yes, because they have common arm OE and common vertex O and their non common arms OC and OD forms a straight line.

(iv) Are ∠BOD and ∠DOA supplementary?

Ans: Yes, ∠BOD and ∠DOA are supplementary because they have a common vertex O and their non common arms form a straight line.

(v) Is ∠1 vertically opposite to ∠4?

Ans: Yes, because they are formed by the intersection of rays AB and CD

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

Ans: ∠COB

10. Indicate which pairs of angles are:

(i) Vertically opposite angles.

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

(ii) Linear pairs.

Ans: ∠1 and ∠5, ∠4 and ∠5 forms linear pairs.

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

Ans: No, because they do not have common vertex.

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

Sol: (i) x = 55° ( vertically opposite angles)

Now ∠x and ∠y forms linear pair

∠x+∠y = 180°

55° + ∠y = 180°

∠y = 180°-55° = 125°

∠y=∠z (vertically opposite angles)

∠z=125°

(ii) ∠z = 40° (vertically opposite angles)

∠y+∠z = 180° (linear pair)

∠y + 40° = 180°

∠y = 180° – 40° = 140°

40°+x+25° = 180° ( Angles on straight line)

x+65° = 180

x = 180° – 65°

= 115°

13. Fill in the blanks:
(i) If two angles are complementary, then the sum of their measures is _90 degrees______.
(ii) If two angles are supplementary, then the sum of their measures is _180 degrees_.
(iii) Two angles forming a linear pair are supplementary___.
(iv) If two adjacent angles are supplementary, they form a linear pair_.
(v) If two lines intersect at a point, then the vertically opposite angles are always
equal_.
(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 _obtuse_______.

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

(i) Obtuse vertically opposite angles

Ans: ∠AOD and ∠BOC

(ii) Adjacent complementary angles

Ans: ∠AOB and ∠EOA

(iii) Equal supplementary angles

Ans: ∠EOB and ∠EOD

(iv) Unequal supplementary angles

Ans: ∠EOA and ∠EOC

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

Ans: ∠COD and∠EOD, ∠AOE and ∠EOD, ∠AOE and ∠AOB

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