*Q.1. Find the complementary angle of each of the following angles:*

*Ans:*

The sum of values of complementary angles is 90°.

(i) 40°

Complement = 90° – 40° = 50°

(ii) 53°

Complement = 90° – 53° = 37°

(iii) 67°

Complement = 90° – 67° = 23°

*Q2. Find the supplementary angle of each of the following angles:*

** Ans**: The sum of values of supplementary angles is 180°

(1)95°

Supplement = 180° – 95° = 85°

(ii) 83°

Supplement = 180° – 83° = 97°

(iii) 155°

Supplement = 180° – 155° = 25°

*Q3: Find out which of following pairs of angles are supplementary and which are complementary.*

* (i) 60°, 120°*

* (ii) 67°, 23°*

* (iii) 108°, 72°*

* (iv) 150°, 30°*

* (v) 50°, 40°*

* (vi) 72°. 18°*

** Ans:** If the sum of measures of angles is 90°, they are complimentary angles. If the sum of measures of angles is 180°, they are known as supplementary angles.

** (i) 60°, 120°**

Sum of value of the above angles = 60° + 120° =180°

The above angles are supplementary.

** (ii) 67°, 23°**

Sum of value of the above angles = 67° + 23° = 90°

The above angles are complementary.

** (iii) 108°, 72°**

Sum of value of the above angles = 108° + 72° =180°

The above angles are supplementary.

** (iv) 150°, 30°**

Sum of value of the above angles =150° + 30° =180°

The above angles are supplementary.

** (v) 50°, 40°**

Sum of value of the above angles = 50° + 40° = 90°

These angles are complementary angles.

** (vi) 72°, 18°**

Sum of value of the above angles = 72° + 18° = 90°

These angles are complementary angles.

*Q4: Determine the angle that is complimentary by itself.*

** Ans:** Let an angle be a.

Let complement of the angle is also a.

If the sum of measures of angle is 90°, it is complimentary angles

a + a = 90°

2a = 90°

a = 90°/2 = 45°

*Q5. Determine the angle that is supplementary by itself.*

** Ans:** Let an angle be a.

Let the supplement of the angle is also a.

If the sum of measures of angle is 180°, it is known as supplementary angle.

a + a = 180°

2a = 180°

a = 90°

*Q6. In the below given figure, ∠1 and ∠2 are supplementary angles. If ∠1 is decreased, what should be the change ∠2 so that it remains supplementary?*

*Ans:*

If

*Q7: Can 2 angles be supplementary if both the angles are:*

** (i) Obtuse?**

** (ii) Acute? **

** (iii) Right?**

*Ans:*

(i) No. Obtuse angle will always be greater than 90. Even if we add the minimum supplementary, it will be more than 180°. So, two obtuse angles can’t be a supplementary angle pair.

(ii) No. Because acute angle will always be lesser than 90°. Even if we add the maximum acute angle i.e, 89, it cannot add up to 180°. So, two acute angles cannot make a supplementary angle pair.

(iii) Yes, The value of right angle= 90° and sum of two right angles make 180°

So, 2 right angles together can make a supplementary angle pair.

*Q8: Find out whether the complementary of an angle greater than 45° is lesser than 45° or greater than 45° or equal to 45°.*

** Ans**: Let X and Y are two angles which make complementary angle pair and X is greater than 45°.

X + Y = 90°

Y = 90° – X

Therefore, B will be lesser than 45°.

**Q9. In the following figure:**

**(a) Is ∠1 adjacent to ∠2?**

**(b) Is ∠AOC adjacent to ∠AOE?**

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

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

**(e) Is ∠1 vertically opposite to ∠1?**

**(f) Which angle is vertically opposite to ∠5?**

*Ans:*

(a) Yes. Because they have a vertex O as common and also arm OC as common. Also, their non-common arms, OA and OE are on either side of the common arm.

(b) No. They have vertex O as common and also arm OA as common. However, their non-common arms, OC and OE are on the same side of the common arm. So, these are not adjacent to each other.

(c) Yes. Since they have vertex O as common and arm OE as common. Also, their non-common arms. OC and OD. are opposite rays.

(d) Yes. Since

(e) Yes. Since these angles are formed by the intersection of two straight lines namely, AB and CD.

(f)

*Q10. Looking at the given diagram below, Identify the following pairs of angles*

* (i) Linear pairs.*

* (ii) Vertically opposite angles.*

** Ans:** (i)

(ii)

*Q11. In the below figure, Is ∠1 adjacent to ∠? ?*

* *

* **Ans:*

*Q12. Find the values of angles A, B and C in each of the following:*

Ans: (i) Since

(ii)

*Q13: Complete the following:*

*(a) The sum of measures of two supplementary angles are ________*

*(b) If 2 adjacent angles are supplementary, they form a ________*

*(c) The sum of measures of two complementary angles are ________ *

*(d) 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*

*(e) The vertically opposite angles are always________, if 2 lines intersect at a point. *

*(f) Two angles forming a linear pair are ________*

*Ans:*

(a) 180°

(b) Linear pair

(c) 90°

(d) Obtuse angles

(e) Equal

(f) Supplementary

*Q14: Name the pairs of angles in the adjoining figure given below.*

(ii) Adjacent complementary angles

(i) Obtuse vertically opposite angles

(iv) Unequal supplementary angles

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

(iii) Equal supplementary angles

**Ans: ** (ii)

(i)

(iv)

(v)

(iii)