Mathematics Class Nine   Class 9 Subject List

Number System
Coordinate Geometry
Polynomials
Linear Equations
Exercise 1
Exercise 2
Exercise 3 & 4
Introduction to Euclid
Lines & Angles
Exercise 1
Exercise 2
Exercise 3
Conrguence in Triangles
Exercise 1
Exercise 2
Exercise 3
Exercise 4
Quadrilaterals
Exercise 1
Exercise 2
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Lines And Angles

Exercise - 1 -

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a = 2/3 b

Or, a = 2/3 x 54º

Or, a = 2 x 18º

Or, a = 36º

Now, b + c = 180º {Angles at a common point on a line}

Or, 54º + c = 180º

Or, c = 180º- 54º

Or, c = 126º

So, c = 126º.

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Question - 4 - In the figure if x + y = w + z, then prove that AOB is a line.

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Given: - x + y = w + z

To Prove: - AOB is a straight line

Proof: - x + y = w + z ………equation (i) {given}

But, x + y + w + z = 360º {Angles around a point}

Or, (x + y) + (w + z) = 360º

Or, (x + y) + (x + y) = 360º {from equation (i)}

Or, x + y + x + y = 360º

Or, 2x + 2y = 360º

Or, 2(x + y) = 360º

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Or, x + y = 180º

Therefore, x and y form a linear pair.

Hence, AOB is a straight line. Proved.

Question5. In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR.

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Solution:  Given: - POQ is a straight line.

OR ┴ PQ

Ray OS meets line PQ at O.

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