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) 20° 

(ii) 35°

(iii) 90°

(iv) 77°

(v) 30°

Solution:

(i) Given an angle 20°

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

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

(ii) Given an angle 35°

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

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

(iii) Given an angle 90°

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

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

(iv) Given an angle 77°

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

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

(v) Given an angle 30°

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

Therefore, its complement 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 complement = 90° 

Thus, its complement 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 complement = 90°

Thus, its complement 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°