Lines and Angles NCERT Solution for Class 7 Maths Chapter 5 Exercise 5.1

Lines and Angles Chapter 5 NCERT Math Ex.-5.1.

 

Exercise 5.1

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

(i)      (ii)        (iii)   

Solution 1:-

  When the sum of the measures of two angles is 90°, the angles are called complementary angles.

Solution (i) Formula :- Complementary Angles = 90° – Given Angle

Complementary of 20° = 90° – 20° = 70°.

Solution (ii) Formula :- Complementary Angles = 90° – Given Angle

Complementary of 63° = 90° – 63° = 27°.

Solution (iii) Formula :- Complementary Angles = 90° – Given Angle

Complementary of 57° = 90° – 57° = 33°.

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

Solution 2:- When two angles are supplementary, each angle is said to be the supplement of the other. 

(i) Formula :- Supplementary Angles = 180° – Given Angle.

(ii) Formula :- Supplementary Angles = 180° – Given Angle.

Supplement of 87° = 180° – 87° = 93°

(iii) Formula :- Supplementary Angles = 180° – Given Angle.

Supplement of 154° = 180° – 154° = 26°

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 3:-

If sum of two angles is 180º , then they are called supplementary angles.

If sum of two angles is 90º , then they are called complementary angles.

(i) 65° (+) 115° = 180°
They are supplementary angles.
(ii) 63° (+) 27° = 90°
They are complementary angles.
(iii) 112° (+) 68° = 180°
They are supplementary angles.
(iv) 130° (+) 50° = 180°
They are supplementary angles.
(v) 45° (+) 45° = 90°
They are complementary angles.
(vi) 80° (+) 10° = 90°
They are complementary angles.

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

Solution 4:
Let the required angle be x°.
its complement = (90 – x)°
Now, re = 90 – x ⇒ x + x = 90
⇒ 2x = 90 ∴ x = 902 = 45°
Thus the required angles are 45°.

Question 5. Find the angle which is equal to its supplement.
Solution 5:
Let the required angle be x°.
∴ it supplement = (180 – x)°
Now, x = 180 – x
⇒ x + x = 180
⇒ 2x = 180°
∴ x=180∘2=90∘
Thus, 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 6:
∠1 + ∠2 = 180° (given)
If ∠1 is decreased by some degrees, then ∠2 will also be increased by the same degree so that the two angles still remain supplementary.

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

Solution7:- 

(i) Since, acute angle < 90°
∴ Acute angle + acute angle < 90° + 90° < 180° Thus, the two acute angles cannot be supplementary angles. (ii) Since, obtuse angle > 90°
∴ Obtuse angle + obtuse angle > 90° + 90° > 180°
Thus, the two obtuse angles cannot be supplementary angles.
(iii) Since, right angle = 90°
∴ right angle + right angle = 90° + 90° = 180°
Thus, two right angles are supplementary angles.

Question 8. An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45 °?
Solution 8:-
Given angle is greater than 45°
Let the given angle be x°.
∴ x > 45
Complement of x° = 90° – x° < 45° [ ∵ x > 45°]
Thus the required angle is less than 45°.

Question 9. 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) If two adjacent angles are supplementary, they form a ______ .

Solution 9:-
(i) 90°
(ii) 180°
(iii) Linear pair.

Question 10. In the given figure, name the following pairs of angles.

(i) Obtuse vertically opposite angles.
(ii) Adjacent complementary angles.
(iii) Equal supplementary angles.
(iv) Unequal supplementary angles.
(v) Adjacent angles but do not form a linear pair.

Solution 10:-
(i) ∠BOC and ∠AOD are obtuse vertically opposite angles.
(ii) ∠AOB and ∠AOE are adjacent complementary angles.
(iii) ∠EOB and ∠EOD are equal supplementary angles.
(iv) ∠EOA and ∠EOC are unequal supplementary angles.
(v) ∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD are adjacent angles but do not form a linear pair.

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