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

• Last Updated : 01 Dec, 2020

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

(i) 20°

(ii) 35°

Attention reader! All those who say programming isn't for kids, just haven't met the right mentors yet. Join the  Demo Class for First Step to Coding Coursespecifically designed for students of class 8 to 12.

The students will get to learn more about the world of programming in these free classes which will definitely help them in making a wise career choice in the future.

(iii) 90°

(iv) 77°

(v) 30°

Solution:

(i) Given an angle 20°

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

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

(ii) Given an angle 35°

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

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

(iii) Given an angle 90°

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

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

(iv) Given an angle 77°

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

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

(v) Given an angle 30°

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

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

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

(i) 54°

(ii) 132°

(iii) 138°

Solution:

Since, Supplement = 2 × (Complement)

Supplement = 2 × (90°)

Therefore, Supplement = 180°

(i) Given an angle 54°

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

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

(ii) Given an angle 132°

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

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

(iii) Given an angle 138°

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

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

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

Solution:

Let the measure of the angle be ‘x’ degrees

As we studied Compliment = 90°

Thus, its Compliment will be (90 – x)°

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 31°

### Question 4: If an angle is 30° 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 Compliment = 90°

Thus, its Compliment will be (90 – x)°

Now,

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

Therefore, our equation will become :

x = 30° + (90 – x)° / 2

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

x + x/2 = 30° + 45°

3x/2 = 75°

x = 50°

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

### 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 = 180°

9x = 180°

x = 20°

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

4x = 4 × (20°) = 80°

5x = 5 × (20°) = 100°

Hence, the required angles are 80° and 100°

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

Solution:

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

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

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 = 66°

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

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

Hence, the two angles are 66° and 114°

### 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 80°

My Personal Notes arrow_drop_up