chapter 6 maths NCERT introduction class 9
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Answer:
Class 9 Maths Chapter 6 Exercise: 6.1 (Page No: 96)
Exercise: 6.1 (Page No: 96)
1. In Fig. 6.13, lines AB and CD intersect at O. If AOC +BOE = 70° and BOD = 40°, find BOE and reflex COE.
Ncert solutions class 9 chapter 6-1
Solution:
From the diagram, we have
(AOC +BOE +COE) and (COE +BOD +BOE) forms a straight line.
So, AOC+BOE +COE = COE +BOD+BOE = 180°
Now, by putting the values of AOC+BOE = 70° and BOD = 40° we get
COE = 110° and
BOE = 30°
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NCERT Solutions for Class 9 Maths Chapter 6 - Lines And Angles
NCERT Solutions for Class 9 Maths Chapter 6 Lines And Angles deals with the questions and answers related to the chapter Lines and Angles. This topic introduces you to the basic Geometry primarily focusing on the properties of the angles formed i) when two lines intersect each other and ii) when a line intersects two or more parallel lines at distinct points.
Now, you must be wondering why we are studying Lines and Angles. What are the real-life applications of it? The answer is that lines and angles are everywhere around us. The architecture uses lines and angles to design the structure of a building. When you stop at a signal and then move on when the signal light is green, then you either take a left angle turn or right-angle turn or move in a straight line. When you have to find the height of a tower or location of an aircraft, then you need to know angles. In NCERT Solutions for Class 9 Maths Chapter 6, you will learn to solve the questions related to all the concepts of Lines and Angles.
You can download the complete solution pdf of NCERT Chapter 6 Line and Angles of Class 9 by clicking on the link below:
Download PDF of NCERT Solutions for Class 9 Maths Chapter 6 – Lines And Angles
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List of Exercises in class 9 Maths Chapter 6
Exercise 6.1 Solutions 6 Questions (5 Short Answer Questions, 1 Long Answer Question)
Exercise 6.2 Solutions 6 Questions (3 Short Answer Questions, 3 Long Answer Question)
Exercise 6.3 Solutions 6 Questions (5 Short Answer Questions, 1 Long Answer Question)
Class 9 Maths Chapter 6 Exercise: 6.1 (Page No: 96)
Exercise: 6.1 (Page No: 96)
1. In Fig. 6.13, lines AB and CD intersect at O. If AOC +BOE = 70° and BOD = 40°, find BOE and reflex COE.
Ncert solutions class 9 chapter 6-1
Solution:
From the diagram, we have
(AOC +BOE +COE) and (COE +BOD +BOE) forms a straight line.
So, AOC+BOE +COE = COE +BOD+BOE = 180°
Now, by putting the values of AOC+BOE = 70° and BOD = 40° we get
COE = 110° and
BOE = 30°
2. In Fig. 6.14, lines XY and MN intersect at O. If POY = 90° and a : b = 2 : 3, find c.
Ncert solutions class 9 chapter 6-2
Solution:
We know that the sum of linear pair are always equal to 180°
So,
POY +a +b = 180°
Putting the value of POY = 90° (as given in the question) we get,
a+b = 90°
Now, it is given that a : b = 2 : 3 so,
Let a be 2x and b be 3x
∴ 2x+3x = 90°
Solving this we get
5x = 90°
So, x = 18°
∴ a = 2×18° = 36°
Similarly, b can be calculated and the value will be
b = 3×18° = 54°
From the diagram, b+c also forms a straight angle so,
b+c = 180°
c+54° = 180°
∴ c = 126°
3. In Fig. 6.15, PQR = PRQ, then prove that PQS = PRT.
Ncert solutions class 9 chapter 6-3
Solution:
Since ST is a straight line so,
∠PQS+∠PQR = 180° (linear pair) and
∠PRT+∠PRQ = 180° (linear pair)
Now, ∠PQS + ∠PQR = ∠PRT+∠PRQ = 180°
Since ∠PQR =∠PRQ (as given in the question)
∠PQS = ∠PRT. (Hence proved).
4. In Fig. 6.16, if x+y = w+z, then prove that AOB is a line.
Ncert solutions class 9 chapter 6-4
Solution:
For proving AOB is a straight line, we will have to prove x+y is a linear pair
i.e. x+y = 180°
We know that the angles around a point are 360° so,
x+y+w+z = 360°
In the question, it is given that,
x+y = w+z
So, (x+y)+(x+y) = 360°
2(x+y) = 360°
∴ (x+y) = 180° (Hence proved).
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