**Question 1: Write the compliment 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 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°

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