Question

"Question 1 In the given figure, find the values of x and y and then show that AB || CD.

Class 9 - Math - Lines and Angles Page 103"

Answer 1

y=130°(Vertically opposite angles)
x=130°(Alternate angle are equal)/(Linear pair)

Answer 2

Parallel lines:

If two lines lie in the same plane and do not intersect when produced on either side then such lines are said to be parallel to each other.

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Transversal line:

A straight line with cuts two or more straight lines at distinct points is called a transversal line.

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Alternate angles:

When two lines are crossed by another line the pair of angles on opposite sides of the transversal is called alternate angles.

 

Theorem 1

If a transversal intersects two Parallel Lines then each pair of alternate interior angles is equal.

Theorem 2

If a transversal intersects two lines such that a pair alternate interior angle is equal then the two lines are parallel.

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Solution:

 

x + 50° = 180° (Linear pair)

 x = 180°- 50°=130°

x=130°

y = 130° (Vertically opposite angles)

x = y = 130° (Alternate interior angles)

 

Alternate interior angles are equal.
Therefore, AB || CD.

[by Theorem 2]

 

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Hope this will help you