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.

BoardCBSE
TextbookNCERT
ClassClass 7
SubjectMaths
ChapterChapter 5
Chapter NameLines and Angles
ExerciseEx 5.1, Ex 5.2.
Number of Questions Solved14
CategoryNCERT Solutions

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:
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 1
Solution:
Since, the sum of the measures of an angle and its complement is 90°, therefore,

  1. The complement of an angle of measure 20° is the angle of (90° – 20°), f.e., 70°.
  2. The complement of an angle of measure 63° is the angle of (90° – 63°), i.e., 27°.
  3. The complement of an angle of measure 57° is the angle of (90° – 57°), i.e., 33°.

Question 2.
Find the supplement of each of the following angles:
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 2
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:

  1. Since, 65°+ 115° = 180°
    So, this pair of angles are supplementary.
  2. Since, 63°+ 27° = 90°
    So, this pair of angles are complementary.
  3. Since, 112° + 68° = 180°
    So, this pair of angles are supplementary.
  4. Since, 130°+50° = 180°
    So, this pair of angles are supplementary.
  5. Since, 45°+ 45° = 90°
    So, this pair of angles are complementary.
  6. Since, 80°+ 10° = 90°
    So, this pair of angles are complementary.

Question 4.
Find the angle which is equal to its complement.
Solution:
Let the measure of the angle be x°. Then, the measure of its complement is given to be x°.
Since, the sum of the measures of an angle and its complement is 90°, therefore,
x° + x° = 90°
⇒ 2x° = 90°
⇒ x° = 45°
Thus, the required angle is 45°.

Question 5.
Find the angle which is equal to its supplement.
Solution:
Let the measure of the angle be x°. Then,
a measure of its supplement = x°
Since, the sum of the measures of an angle and its supplement is 180°, therefore,
x° + x° = 180°
⇒ 2x° =180°
⇒ x° = 90°
Hence, the required angle is 90°.

Question 6.
In the given figure, ∠ 1 and ∠ 2 are supplementary angles.
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 3
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 a 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:
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°.

Question 9.
In the adjoining figure:
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 4

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

  1. Vertically opposite angles.
  2. Linear pairs.

Solution:

  1. The pair of vertically opposite angles are ∠1, ∠4; ∠5, ∠2 + ∠3.
  2. The pair of linear angles are ∠1, ∠5; ∠4, ∠5.

Question 11.
In the following figure, is ∠ 1 adjacent to ∠ 2? Give reasons.
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 6
Solution:
∠1 is not adjacent to ∠2 because they have no common vertex.

Question 12.
Find the values of the angles x, y, and z in each of the following:
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 7
Solution:
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 8

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.
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles Ex 5.1 9

  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. Obtuse vertically opposite angles are ∠AOD and ∠BOC.
  2. Adjacent complementary angles are ∠BOA and ∠AOE.
  3. Equal supplementary angles are ∠BOE and ∠EOD.
  4. Unequal supplementary angles are ∠BOA and ∠AOD, ∠BOC and ∠COD, ∠EOA, and ∠EOC.
  5. Adjacent angles that do not form a linear pair are ∠AOB and ∠AOE, ∠AOE and ∠EOD; ∠EOD and ∠COD.

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