Chapter -5 Lines and Angles | Class 7th |NCERT Maths Solutions | Edugrown

Ex 5.1 Class 7 Maths 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°

Ex 5.1 Class 7 Maths Question 2.
Find the supplement of each of the following angles :

Solution:
Since, the sum of the measures of an angle and its supplement is 180°, therefore,

1. The supplement of an angle of measure 105° is the angle of (180°-105°), i.e., 75°.
2. The supplement of an angle of measure 87° is the angle of (180°-87°), i.e., 93°.
3. The supplement of an angle of measure 154° is the angle of (180°-154°), i.e., 26°.

Ex 5.1 Class 7 Maths Question 3.
Identify which of the following pairs of angles are complementary and which are supplementary :
(i) 65°, 115°
(ii) 63°, 27°
(iii) 112°, 68°
(iv) 130°, 50°
(v) 45°, 45°
(vi) 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.

Ex 5.1 Class 7 Maths 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° = 90∘3 = 45°

Ex 5.1 Class 7 Maths 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° = 180∘3 = 90°
Hence, the required angle is 90°.

Ex 5.1 Class 7 Maths 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 with the same measure as the decrease in ∠1.

Ex 5.1 Class 7 Maths Question 7.
Can two angles be supplementary if both of them are :

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

Solution:

1. No
2. No
3. Yes

Ex 5.1 Class 7 Maths Question 8.
An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?
Solution:
Since the sum of the measure of ah angle and its complement is 90°.
∴ The complement of an angle of measures 45° + x°,
where x > 0 is the angle of [90° – (45° + x°)] = 90° – 45° – x°= 45° – x°.
Clearly, 45° + x° > 45° – x°
Hence, the complement of an angle > 45° is less than 45°.

Ex 5.1 Class 7 Maths 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 Z4?
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.

Ex 5.1 Class 7 Maths 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

Ex 5.1 Class 7 Maths Question 11.
In the adjoining figure, is ∠1 adjacent to ∠2? Give reasons.

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

Ex 5.1 Class 7 Maths Question 12.
Find the values of the angles x, y, and z in each of the following?

Solution:

Ex 5.1 Class 7 Maths 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

Ex 5.1 Class 7 Maths 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 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.

Ex 5.2 Class 7 Maths Question 1.
State the property that is used in each of the following statements?

Solution:
(i) Corresponding angle property.
(ii) Alternate interior angle property.
(iii) Interior angles on the same side of the transversal are supplementary.

Ex 5.2 Class 7 Maths Question 2.
In the adjoining figure, identify :

1. the pairs of corresponding angles.
2. the pairs of alternate interior angles.
3. the pairs of interior angles on the same side of the transversal.
4. the vertically opposite angles

Solution:

1. ∠1, ∠5; ∠2, ∠6; ∠3, ∠7 and ∠4, ∠8 are four pairs of corresponding angles.
2. ∠2, ∠8 and ∠3, ∠5 are two pairs of alternate interior angles.
3. ∠2, ∠5 and ∠3, ∠8 are two pairs of interior angles on the same side of the transversal.
4. ∠1, ∠3; ∠2, ∠4; ∠5, ∠7 and ∠6, ∠8 are four pairs of vertically opposite angles.

Ex 5.2 Class 7 Maths Question 3.
In the adjoining figure p || q. Find the unknown angles

Solution:

Ex 5.2 Class 7 Maths Question 4.
Find the value of x in each of the following figures if l || m :

Solution:
(i) Since, l || m and t is a transversal.
∴ ∠x = (180° – 110°) = 70° [Corresponding angles, Linear pair]

(ii) if l || m and a is a transversal.
Then, ∠x = 1000 [Corresponding angles]

Ex 5.2 Class 7 Maths Question 5.
In the given figure, the arms of two angles are parallel. If ∠ABC = 70°, then find

(i) DGC
(ii) DEF
Solution:

Ex 5.2 Class 7 Maths Question 6.
In the given figures below, decide whether l is parallel to m.

Solution: