Class 9 Exam  >  Class 9 Notes  >  RD Sharma Solutions for Class 9 Mathematics  >  RD Sharma Solutions Ex-8.1, Lines And Angles, Class 9, Maths

RD Sharma Solutions Ex-8.1, Lines And Angles, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics PDF Download

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
  • RD Sharma Solutions Ex-8.1, Lines And Angles, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics
  • 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

RD Sharma Solutions Ex-8.1, Lines And Angles, Class 9, Maths | RD Sharma Solutions for Class 9 Mathematics

  • (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

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

1. What are the types of angles?
Ans. There are various types of angles such as acute angle, right angle, obtuse angle, straight angle, reflex angle, and full angle.
2. How do you identify complementary angles?
Ans. Complementary angles are two angles whose sum is equal to 90 degrees. To identify complementary angles, you can add the measures of the angles. If the sum is 90 degrees, then the angles are complementary.
3. What is the difference between adjacent angles and linear pair angles?
Ans. Adjacent angles are two angles that share a common vertex and a common side but do not overlap. On the other hand, linear pair angles are adjacent angles that form a straight line when combined. In other words, the sum of the measures of linear pair angles is always equal to 180 degrees.
4. How do you find the measure of an angle using a protractor?
Ans. To find the measure of an angle using a protractor, place the center of the protractor on the vertex of the angle. Align one side of the angle with the 0-degree mark on the protractor. Then, read the measure of the angle where the other side intersects the protractor scale.
5. Can two obtuse angles be adjacent angles?
Ans. No, two obtuse angles cannot be adjacent angles. Adjacent angles share a common vertex and a common side, but they cannot overlap. Since obtuse angles are greater than 90 degrees, it is not possible for two obtuse angles to share a common side without overlapping.
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