# 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.