## Chapter 5 Lines and Angles Exercise 5.1

**Question 1: Find the complement of each of the following angles:(i)**

**Answer: **

Given angle = 20°

Complementary angle = ?

Complementary angle = 90°

= 90° - 20° = 70°**(ii)**

**Answer:**

Given angle = 63°

Complementary angle = ?

Complementary angle = 90°

= 90° - 63° = 27°**(iii)**

**Answer: **

Given angle = 57°

Complementary angle = ?

Complementary angle = 90°

= 90° - 57° = 33°**Question 2: Find the supplement of each of the following angles:(i)**

**Answer: **

Given angle = 105°

Supplementary angle = ?

Supplementary angle = 180°

= 180° - 105° = 75°**(ii)**

**Answer: **

Given angle = 87°

Supplementary angle = ?

Supplementary angle = 180°

= 180° - 87° = 93°**(iii)**

**Answer:**

Given angle = 154°

Supplementary angle = ?

Supplementary angle = 180°

= 180° - 154° = 26°**Question 3: Identify which of the following pairs of angles are complementary and which are supplementary.(i) 65°, 115°Answer:**

Complementary angle = 90°

65° + 115° = 180° ≠ 90°

Supplementary angle = 180°

65° + 115° = 180° = 180°

Therefore, this is a supplementary angle.

(ii) 63°, 27°

Answer:

(ii) 63°, 27°

Answer:

Complementary angle = 90°

63° + 27° = 90° = 90°

Supplementary angle = 180°

63° + 27° = 90° ≠ 180°

Therefore, this is a complementary angle.

**(iii) 112°, 68°**

Answer:

Answer:

Complementary angle = 90°

112° + 68° = 180° ≠ 90°

Supplementary angle = 180°

112° + 68° = 180° = 180°

Therefore, this is a supplementary angle.

**(iv) 130°, 50°**

Answer:

Answer:

Complementary angle = 90°

130° + 50° = 180° ≠ 90°

Supplementary angle = 180°

130° + 50° = 180° = 180°

Therefore, this is a supplementary angle.

**(v) 45°, 45°**

Answer:

Answer:

Complementary angle = 90°

45° + 45° = 90° = 90°

Supplementary angle = 180°

45° + 45° = 90° ≠ 180°

Therefore, this is a complementary angle.

**(vi) 80°, 10°**

Answer:

Answer:

Complementary angle = 90°

80° + 10° = 90° = 90°

Supplementary angle = 180°

80° + 10° = 90° ≠ 180°

Therefore, this is a complementary angle.

**Question 4: Find the angles which is equal to its complement.**

Answer:

Answer:

Complementary angle = 90°

= a + a = 90°

= 2a = 90°

= a = 90/2

= a = 45°

**Question 5: Find the angles which is equal to its supplement.**

Answer:

Answer:

Supplementary angle = 180°

= a + a = 180°

= 2a = 180°

= a = 180/2

= a = 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 angles still remain supplementary.**

**Answer:**

If ∠1 is decreased then ∠2 will increase with same measurement, so that both the angles still remain supplementary. Example: ∠1 = 80° while ∠2 = 100°.

If ∠1 is decreases to 60° then ∠2 will increase to 120°.

If ∠1 increases to 95° then ∠2 will decrease to 85°.

**Question 7: Can two angles be supplementary if both of them are:**

(i) Acute?

Answer:No, because the sum of two acute angles is less than 180°.

(i) Acute?

Answer:

**(ii) Obtuse?**

Answer:No, because the sum of two obtuse angles is more than 180°.

Answer:

**Yes, because the sum of two right angles is equal to 180°.**

(iii) Right?

Answer:

(iii) Right?

Answer:

**Question 8: An angle is greater than 45°. Is its complementary angle greater than 45° or equal to 45° or less than 45°?**

Answer:

Answer:

Let complementary angles be x and y. Therefore, x + y = 90°.

It is given that x > 45°

Adding y on both the sides

= x + y > 45° + y

= 90° > 45° + y

= 90° - 45° > y

= y < 45°

Therefore, its complementary angle is less than 45°.

**Question 9: In the adjoining figure:**

**(i) Is ∠1 adjacent to ∠2?**

Answer:Yes, as ∠1 and ∠2 share a common arm i.e. OC.

Answer:

**(ii) Is ∠AOC adjacent to ∠AOE?**

Answer:No, as they have no common arm on opposite side of common arm.

Answer:

**(iii) Do ∠COE and ∠EOD form a linear pair?**

Answer:Yes, they form a linear pair.

Answer:

**(iv) Are ∠BOD and ∠DOA supplementary?**

Answer:Yes, they are supplementary.

Answer:

**(v) Is ∠1 vertically opposite to ∠4?**

Answer:Yes, ∠1 is vertically opposite angle ∠4.

Answer:

**(vi) What is the vertically opposite angle of ∠5?**

Answer:Vertically opposite angles of ∠5 is ∠3 + ∠2 (∠COB).

Answer:

**Question 10: Indicate which pairs of angles are:**

**(i) Vertically opposite angles.**

Answer:∠1 and ∠4, ∠5 and ∠3 + ∠2

Answer:

**(ii) Linear pairs.**

Answer:∠1 and ∠5, ∠4 and ∠5

Answer:

**Question 11: In the following figure, is ∠1 adjacent to ∠2? Give reasons.**

**Answer:**No, ∠1 and ∠2 are not adjacent as they don’t have a common vertex.

**Question 12: Find the values of the angles x, y, and z in each of the following:**

(i)

(i)

**Answer:**

x = 55° (as they are vertically opposite angles)

So, x = 55°.

x + y = 180° (as they form a linear pair)

= 55° + y = 180°

= y = 180° - 55° = 125°

So, y = 125°.

z = 125° (as they are vertically opposite angles)

So, z = 125°.

**(ii)**

**Answer:**

40° + x + 25° = 180° (angles on a straight line)

= 65° + x = 180°

= x = 180° - 65°

= x = 115°

So, x = 115°.

∠y = ∠x + 25° (vertically opposite angles)

= ∠y = 115° + 25°

= ∠y = 140°

So, ∠y = 140°.

∠z = 40° (vertically opposite angles)

So, ∠z = 40°.

**Question 13: Fill in the blanks:**

(i) If two angles are complementary, then the sum of their measures is

(i) If two angles are complementary, then the sum of their measures is

__90°__

**.**

(ii) If two angles are supplementary, then the sum of their measures is

(ii) If two angles are supplementary, then the sum of their measures is

__180°__

**.**

(iii) Two angles forming a linear pair are

(iii) Two angles forming a linear pair are

__supplementary__

**.**

(iv) If two adjacent angles are supplementary, they form a

(iv) If two adjacent angles are supplementary, they form a

__linear pair__

**.**

(v) If two lines intersect at a point, then the vertically opposite angles are always

(v) If two lines intersect at a point, then the vertically opposite angles are always

__equal__

**.**

(vi) 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

(vi) 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

__obtuse__

**.**

**Question 14: In the adjoining figure, name the following pairs of angles.**

**(i) Obtuse vertically opposite angles**

Answer:∠AOD and ∠BOC are obtuse vertically opposite angles in the given figure.

Answer:

**(ii) Adjacent complementary angles**

Answer:∠EOA and ∠AOB are adjacent complementary angles in the given figure.

Answer:

**(iii) Equal supplementary angles**

Answer:∠EOB and EOD are the equal supplementary angles in the given figure.

Answer:

**(iv) Unequal supplementary angles**

Answer:∠EOA and ∠EOC are the unequal supplementary angles in the given figure.

Answer:

**(v) Adjacent angles that do not form a linear pair**

Answer:∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD are the adjacent angles that do not form a linear pair in the given figure.

Answer:

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