RD Sharma Solutions for Class 9 Maths are given here for Chapter 8 – Lines and Angles. In order to make concepts easier for students, we are providing RD Sharma Class 9 Maths Chapter 8 solutions to help them go through several solved exercises and at the same time practice the questions. The RD Sharma solutions for class 9 can help students discover new ways to solve difficult problems. Students can download RD Sharma Class 9 solutions and practice offline.

## Download PDF of RD Sharma Solutions for Class 9 Maths Chapter 8 Lines and Angles Exercise 8.1

### Access Answers to Maths RD Sharma Class 9 Chapter 8 Lines and Angles Exercise 8.1 Page number 8.7

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

** (i)20 ^{0} **

**(ii)35 ^{0}**

**(iii)90 ^{0} **

**(iv) 77 ^{0} **

**(v)30 ^{0}**

**Solution**:

**(i)** The sum of an angle and its complement = 90^{0}

Therefore, the complement of 20** ^{0 }**= 90

**â€“ 20**

^{0}**= 70**

^{0}

^{0}**(ii)** The sum of an angle and its complement = 90^{0}

Therefore, the complement of 35Â° = 90Â° â€“ 35Â° = 55

**(iii)** The sum of an angle and its complement = 90^{0}

Therefore, the complement of 90** ^{0}** = 90

**â€“ 90**

^{0}**= 0**

^{0}

^{0}**(iv)** The sum of an angle and its complement = 90^{0}

Therefore, the complement of 77** ^{0}** = 90Â° â€“ 77

**= 13**

^{0}

^{0}**(v)** The sum of an angle and its complement = 90^{0}

Therefore, the complement of 30** ^{0}** = 90

**â€“ 30**

^{0}**= 60**

^{0}

^{0}**Question 2 : Write the supplement of each of the following angles:**

** (i) 54 ^{0}**

**(ii) 132 ^{0}**

** (iii) 138 ^{0}**

**Solution:**

**(i)** The sum of an angle and its supplement = 180** ^{0}**.

Therefore supplement of angle 54** ^{0}** = 180

**â€“ 54**

^{0}**= 126**

^{0}

^{0}**(ii)** The sum of an angle and its supplement = 180** ^{0}**.

Therefore supplement of angle 132** ^{0}** = 180

**â€“ 132**

^{0}**= 48**

^{0}

^{0}**(iii)** The sum of an angle and its supplement = 180** ^{0}**.

Therefore supplement of angle 138** ^{0 }**= 180

**â€“ 138**

^{0 }**= 42**

^{0}

^{0}**Question 3: If an angle is 28 ^{0} less than its complement, find its measure?**

**Solution:**

Let the measure of any angle is â€˜ a â€˜ degrees

Thus, its complement will be (90 â€“ a)^{ 0}

So, the required angle = Complement of a â€“ 28

a = ( 90 â€“ a ) â€“ 28

2a = 62

a = 31

Hence, the angle measured is 31** ^{0}**.

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

**Solution**:

Let an angle measured by â€˜ a â€˜ in degrees

Thus, its complement will be (90 – a)^{ 0}

Required Angle = 30** ^{0}** + complement/2

a = 30** ^{0}** + ( 90 â€“ a )

**/ 2**

^{ 0}a + a/2 = 30** ^{0}** + 45

^{0}3a/2 = 75^{0}

a = 50^{0}

Therefore, the measure of required angle is 50** ^{0}**.

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

**Solution**:

Two supplementary angles are in the ratio 4:5.

Let us say, the angles are 4a and 5a (in degrees)

Since angle are supplementary angles;

Which implies, 4a + 5a = 180^{0}

9a = 180^{0}

a = 20^{0}

Therefore, 4a = 4 (20) = 80** ^{0 }**and

5(a) = 5 (20) = 100^{0}

Hence, required angles are 80Â° and 100** ^{0}**.

**Question 6 : Two supplementary angles differ by 48 ^{0}. Find the angles?**

**Solution**: Given: Two supplementary angles differ by 48** ^{0}**.

Consider a** ^{0}** be one angle then its supplementary angle will be equal to (180 â€“ a)

^{ 0}According to the question;

(180 â€“ a ) â€“ x = 48

(180 â€“ 48 ) = 2a

132 = 2a

132/2 = a

Or a = 66^{0}

Therefore, 180 â€“ a = 114^{0}

Hence, the two angles are 66** ^{0}** and 114

**.**

^{0}**Question 7: An angle is equal to 8 times its complement. Determine its measure?**

**Solution:** Given: Required angle = 8 times of its complement

Consider a** ^{0}** be one angle then its complementary angle will be equal to (90 â€“ a)

^{ 0}According to the question;

a = 8 times of its complement

a = 8 ( 90 â€“ a )

a = 720 â€“ 8a

a + 8a = 720

9a = 720

a = 80

Therefore, the required angle is 80** ^{0}**.

## RD Sharma Solutions for Class 9 Maths Chapter 8 Exercise 8.1

Class 9 Maths Chapter 8 Lines and Angles Exercise 8.1 is based on the following topics and subtopics:

- Angles
- Interior of an angle
- Exterior of an angle
- Congruent angles
- Measure of an angle
- Axioms and Theorems
- Types of angles
- -Right Angle
- -Acute Angle
- -Obtuse Angle
- -Straight Angle
- -Reflex Angle
- -Complementary Angles
- -Supplementary Angles

- Angle Bisector