**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.