NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1, are part of NCERT Solutions for Class 7 Maths. Here we have given NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1.

NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1

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

Solution:

1. Complement of the angle 20° = 90° – 20° = 70°
2. Complement of the angle 63° = 90° – 63° = 27°
3. Complement of the angle 57° = 90° – 57° = 33°.

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

Solution:

1. Supplement of the angle 105° = 180° – 105° = 75°
2. Supplement of the angle 87° = 180° – 87° = 93°
3. Supplement of the angle 154° = 180° – 154° = 26°.

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

1. 65°, 115°
2. 63°, 27°
3. 112°, 68°
4. 130°, 50°
5. 45°,45°
6. 80°, 10°.

Solution:
(i) 65°, 115°
∵ 65° + 115° = 180°
∴ The given pair of angles are supplementary.

(ii) 63°, 27°
∵ 63° + 27° = 90°
The given pair of angles are complementary.

(iii) 112°, 68°
∵ 112° + 68° = 180°
∴ The given pair of angles are supplementary.

(iv) 130°, 50°
∵ 130° + 50° = 180°
∴ The given pair of angles are supplementary.

(v) 45°, 45°
∵45° + 45° = 90°
∴ The given pair of angles are complementary.

(vi) 80°, 10°
∵ 80° + 10° = 90°
∴ The given pair of angles are complementary.

Question 4.
Find the angle which is equal to its complement.
Solution:
Let the angle be x°.
Its complement = 90° – x°
According to the question,
x° = 90° – x0
⇒ x° + x° = 90°
⇒ 2x° = 90°
⇒ x° = \(\frac { { 90 }^{ \circ } }{ 3 }\) = 45°

Question 5.
Find the angle which is equal to its supplement.
Solution:
Let the angle be x°.
Its supplement = 180° – x°
According to the question,
x° = 180° – x°
⇒ x° + x° = 180°
⇒ 2x° = 180°
⇒ x° = \(\frac { { 180 }^{ \circ } }{ 3 }\) = 90°
Hence, the required angle is 90°.

Question 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.
Solution:
∠ 2 will increase as much as ∠ 1 decreases.

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

1. acute ?
2. obtuse ?
3. right ?

Solution:

1. No ! two acute angles cannot be supplement
2. No ! Two obtuse angles cannot be supplementary.
3. Yes ! Two right angles are always supplementary.

Question 8.
An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°.
Solution:
Its complementary angle is less than 45°.

Question 9.
In the adjoining figure:

1. Is ∠1 adjacent to ∠2 ?
2. Is ∠ AOC adjacent to ∠ AOE ?
3. Do ∠ COE and ∠ EOD form a linear pair ?
4. Are ∠ BOD and ∠ DOA supplementary ?
5. Is ∠ 1 vertically opposite to ∠ 4 ?
6. What is the vertically opposite angle of ∠ 5 ?

Solution:

1. Yes ! ∠ 1 is adjacent to ∠ 2.
2. No ! ∠ AOC is not adjacent to ∠ AOE.
3. Yes! ∠ COE and ∠ EOD form a linear pair.
4. Yes ! ∠ BOD and ∠ DOA are supplementary.
5. Yes ! ∠ 1 is vertically opposite to ∠ 4.
6. The vertically opposite angle of ∠ 5 is ∠ 2 + ∠ 3, i.e., ∠ COB.

Question 10.
Indicate which pairs of angles are:

1. Vertically opposite angles.
2. Linear pairs.

Solution:

1. ∠ 1 and ∠ 4 ; ∠ 5 and ∠ 2 + ∠ 3
2. ∠ 4 and ∠ 5 ; ∠ 5 and ∠ 1

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

Solution:
No ! ∠ 1 is not adjacent to ∠ 2 because their vertex is not common.

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

Solution:

Question 13.
Fill in the blanks:

1. If two angles are complementary, then the sum of their measures is
2. If two angles are supplementary, then the sum of their measures is
3. Two angles forming a linear pair are
4. If two adjacent angles are supplementary, they form a
5. If two lines intersect at a point, then the vertically opposite angles are always
6. 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:

1. 90°
2. 180°
3. supplementary
4. linear pair
5. equal
6. obtuse angles

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

1. Obtuse vertically opposite angles
2. Adjacent complementary angles
3. Equal supplementary angles
4. Unequal supplementary angles
5. Adjacent angles that do not form a linear pair.

Solution:

1. ∠ AOD and ∠ BOC
2. ∠ EOA and ∠ AOB
3. ∠ BOE and ∠ DOE
4. ∠ EOC and ∠ EOA
5. ∠ AOB and ∠ AOE ; ∠ AOE and ∠ EOD ; ∠ EOD and ∠ DOC.

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