# Class 9 RD Sharma Solutions – Chapter 8 Introduction to Lines and Angles- Exercise 8.1

### Question 1: Write the complement of each of the following angles:

(i) 20Â°

(ii) 35Â°

(iii) 90Â°

(iv) 77Â°

(v) 30Â°

Solution:

(i) Given an angle 20Â°

As we Studied in this Chapter, the sum of angle and its complement is 90

Therefore, its complement will be (90Â° – 20Â° = 70Â°)

(ii) Given an angle 35Â°

As we Studied in this Chapter, the sum of angle and its complement is 90

Therefore, its complement will be (90Â° – 35Â° = 55Â°)

(iii) Given an angle 90Â°

As we Studied in this Chapter, the sum of angle and its complement is 90

Therefore, its complement will be (90Â° – 90Â° = 0Â°)

(iv) Given an angle 77Â°

As we Studied in this Chapter, the sum of angle and its complement is 90

Therefore, its complement will be (90Â° – 77Â° = 33Â°)

(v) Given an angle 30Â°

As we Studied in this Chapter, the sum of angle and its complement is 90

Therefore, its complement will be (90Â° – 30Â° = 70Â°)

### Question 2: Write the supplement of each of the following angles:

(i) 54Â°

(ii) 132Â°

(iii) 138Â°

Solution:

Since, Supplement = 2 Ã— (Complement)

Supplement = 2 Ã— (90Â°)

Therefore, Supplement = 180Â°

(i) Given an angle 54Â°

As we have Studied, the sum of angle and its Supplement is 180Â°

Therefore, Supplement of angle 54Â° will be (180Â° – 54Â° = 126Â°)

(ii) Given an angle 132Â°

As we have Studied, the sum of angle and its Supplement is 180Â°

Therefore, Supplement of angle 132Â° will be (180Â° – 132Â° = 48Â°)

(iii) Given an angle 138Â°

As we have Studied, the sum of angle and its Supplement is 180Â°

Therefore, Supplement of angle 54Â° will be (180Â° – 138Â° = 42Â°)

### Question 3: If an angle is 28Â° less than its complement, find its measure?

Solution:

Let the measure of the angle be ‘x’ degrees

As we studied complement = 90Â°

Thus, its complement will be (90 – x)Â°

Now,

The required angle = Complement of x – 28;

Therefore, our equation will become :

x = (90 – x) – 28

Now, after shifting x to left side, our equation will become:

2x = 62

x = 31

Therefore, the measure of the required angle will be 31Â°

### Question 4: If an angle is 30Â° more than one half of its complement, find the measure of the angle?

Solution:

Let the measure of the angle be ‘x’ degrees

As we studied complement = 90Â°

Thus, its complement will be (90 – x)Â°

Now,

The required angle = 30Â° + (Complement)/2 ;

Therefore, our equation will become :

x = 30Â° + (90 – x)Â° / 2

Now we will shift x to left side so 90 is also divided by 2 then our equation will become :

x + x/2 = 30Â° + 45Â°

3x/2 = 75Â°

x = 50Â°

Therefore, the measure of the required angle will be 50Â°

### Question 5: Two supplementary angles are in the ratio 4:5. Find the angles?

Solution:

As given in the question Two Supplementary angles are in ratio 4 : 5

Assume, the angles are 4x and 5x (in degrees)

As we know both are supplementary angles,

Therefore, our equation will become 4x + 5x = 180Â°

9x = 180Â°

x = 20Â°

Now we put the value of x in both the angles i.e 4x and 5x

4x = 4 Ã— (20Â°) = 80Â°

5x = 5 Ã— (20Â°) = 100Â°

Hence, the required angles are 80Â° and 100Â°

### Question 6: Two supplementary angles differ by 48Â°. Find the angles?

Solution:

As given in the question itself Two Supplementary angle differ by 48Â°

Consider x be one angle then its Supplementary angle will be equal to (180 – x)Â°

So, According to the question:

(180 – x) – x = 48

Now Shifting x to right side and 48 to left side then we get

(180 – 48) = 2x

2x = 132

x = 132 / 2

x = 66Â°

Now we find the second angle by putting the value of x i.e (180 – x)

Therefore, the second angle = 180 – 66 = 114Â°

Hence, the two angles are 66Â° and 114Â°

### Question 7: An angle is equal to 8 times its Complement. Determine its measure?

Solution:

According to the question, Required Angle = 8 times of its Complement

Let’s take x be one angle , then its Complementary angle will be (90 – x)

Now, as the question say our equation will become

x = 8 times of its complement

x = 8 (90 – x)

x = 720 – 8x

Now shifting 8x to left side we get,

x + 8x = 720

9x = 720

x = 80

Hence, the Required Angle is 80Â°

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