The document RD Sharma Solutions Ex-8.1, Lines And Angles, Class 9, Maths Class 9 Notes | EduRev is a part of the Class 9 Course RD Sharma Solutions for Class 9 Mathematics.

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**Q 1 : Write the complement of each of the following angles:**

**(i)20 ^{∘} (ii)35^{∘} (iii)90^{∘} (iv)77^{∘} (v)30^{∘}**

**Ans : (i) **given angle is 20

Since, the sum of an angle and its compliment is 90

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

**(ii) **Given angle is 35

Since, the sum of an angle and its compliment is 90

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

**(iii) **Given angle is 90

Since, the sum of an angle and its compliment is 90

Hence, its compliment will be (90 – 90 = 0)

**(iv)** Given angle is 77

Since, the sum of an angle and its compliment is 90

Hence, its compliment will be (90 – 77 = 13)

**(v)** Given angle is 30

Since, the sum of an angle and its compliment is 90

Hence, its compliment will be (90 – 30 = 60)

**Q 2 : Write the supplement of each of the following angles:**

**(i) 54 ^{∘} (ii) 132^{∘} (iii) 138^{∘}**

**Ans : (i) **The given angle is 54,

Since the sum of an angle and its supplement is 180,

Hence, Its supplement will be (180 – 54 = 126)

**(ii)** The given angle is 132,

Since the sum of an angle and its supplement is 180,

Hence, its supplement will be 180 – 132 = 48

**(iii)** The given angle is 138,

Since the sum of an angle and its supplement is 180,

Hence, Its supplement will be 180 – 138 = 42

**Q 3 : If an angle is 28 ^{∘} less than its complement, find its measure?**

**Ans: **Let the angle measured be ‘ x ‘ in degrees

Hence, Its complement will be 90−x^{∘}

- Angle = Complement – 28
- x = (90 – x) – 28
- 2x = 62
- x = 31

Therefore, angle measured is 31^{∘}

**Q 4 : If an angle is 30 ^{∘} more than half of its complement, find the measure of the angle?**

**Ans : **Let the measured angle be ‘x‘

Hence its complement will be (90-x)

It is given that,

Angle =30 + complement/2

- x = 30 + (90 – x) / 2
- 3x = 150
- x = 50

Therefore the angle is 50^{∘}

**Q 5 : Two supplementary angles are in the ratio 4:5.Find the angles?**

**Ans : **Supplementary angles are in the ratio 4:5

Let the angles be 4x and 5x

It is given that they are supplementary angles

Hence 4x + 5x = 180

- 9x = 180
- x = 20

Hence, 4x = 4 (20) = 80

5(x) = 5 (20) = 100

Hence, angles are 80 and 100

**Q 6 : Two supplementary angles differ by 48∘.Find the angles ?**

**Ans : **Given that two supplementary angles differ by 48^{∘}

Let the angle measured be x∘

Therefore, Its supplementary angle will be (180−x)^{∘} ** **

It is given that :

- (180 – x) – x = 48
- (180 – 48) = 2x
- 2 x = 132
- x = 132/2
- x = 66

Hence, 180 – x = 114^{∘}

Therefore, the angles are 66 and 114.

**Q 7 : An angle is equal to 8 times its complement. Determine its measure?**

**Ans : **It is given that required angle = 8 times its complement

Let ‘ x ‘ be the measured angle

- angle = 8 times complement
- angle = 8 (90 – x)
- x = 8 (90 – x )
- x = 720 – 8x
- x + 8x = 720
- 9x = 720
- x = 80

Therefore measured angle is 80.

**Q 8 : If the angles (2x−10) ^{∘} and (x−5)^{∘} are complementary, find x ?**

**Ans : **Given that (2x−10)∘ and (x−5)∘ are complementary

Since angles are complementary, their sum will be 90

- (2x – 10) + (x – 5) = 90
- 3x -15 = 90
- 3x = 90 + 15
- 3x = 105
- x = 105/3
- x = 35

Hence, the value of x = (35)^{∘}

**Q 9 : If the compliment of an angle is equal to the supplement of Thrice of itself, find the measure of the angle ?**

**Ans : **Let the angle measured be ‘ x ‘ say.

Its complementary angle is (90 – x) and

Its supplementary angle is (180 – 3x)

Given that, Supplementary of 4 times the angle = (180 – 3x)

According to the given information;

- (90 – x) = (180 – 3x)
- 3x – x = 180 – 90
- 2x = 90
- x = 90/2
- x = 45

Therefore, the measured angle x = (45)^{∘}

**Q 10 : If an angle differs from its complement by (10) ^{∘}, find the angle ?**

**Ans : **Let the measured angle be ‘ x ‘ say

Given that,

The angles measured will differ by (20)^{∘}

x – (90 – x) = 10

- x – 90 + x = 10
- 2x = 90 + 10
- 2x = 100
- x = 100/2
- x = 50

Therefore the measure of the angle is (50)^{∘}

**Q 11 : If the supplement of an angle is 3 times its complement, find its angle ?**

**Ans : **Let the angle in case be ‘ x ‘

** **Given that,

Supplement of an angle = 3 times its complementary angle

Supplementary angle = 180 – x

Complementary angle = 90 – x

Applying given data,

- 180 – x = 3 (90 –x)
- 3x – x = 270 – 180
- 2x = 90
- x = 90/2
- x = 45

Therefore, the angle in case is 45^{∘}

**Q 12 : If the supplement of an angle is two third of itself. Determine the angle and its supplement?**

**Ans: **Supplementary of an angle = 2/3 angle

Let the angle in case be ‘ x ’,

Supplementary of angle x will be ( 180 – x)

It is given that

- (180 – x) 3 = 2x
- 540 -3x = 2x
- 5x = 540
- x = 540/5
- x = 108

Hence, supplementary angle = 180 – 108 = 72

Therefore, angles in case are 108^{∘} and supplementary angleis 72^{∘}

**Q 13 : An angle is 14 ^{∘} more than its complementary angle. What is its measure?**

**Ans: **Let the angle in case be ‘ x ’,

Complementary angle of ‘ x ’ is ( 90 – x)

From given data,

x – (90 – x) = 14

- x – 90 +x = 14
- 2x = 90 + 14
- 2x = 104
- x =104/2
- x = 52

Hence the angle in case is found to be 52∘

**Q 14 : The measure of an angle is twice the measure of its supplementary angle. Find the measure of the angles?**

**Ans :** Let the angle in case be ‘ x ’

The supplementary of a angle x is (180 – x)

Applying given data:

x = 2 (180 –x)

- x = 360 -2x
- 3x = 360
- x = 360/3
- x = 120

Therefore the value of the angle in case is 120^{∘}