"Question 2 In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x.
Class 9 - Math - Lines and Angles Page 104"
Answers
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.
Interior angles on the same side of the transversal:
The pair of interior angles on the same side of the transversal are called consecutive interior angles or allied angles or co interior angles.
If a transversal intersects two Parallel Lines then each pair of interior angles on the same side of the transversal is supplementary.
If a transversal intersects two lines such that a pair of alternate interior angles is equal then the two lines are parallel.
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Given :
AB∥CD & CD∥EF
AB∥EF
[ as lines parallel to the same line are parallel to each other]
x=z ………….(i)
[alternate interior angles]
x+y=180∘ …………(ii)
[consecutive interior angles on the same side of the transversal ]
From (i) and (ii), we have
z+y=180°.........(iii)
y:z=3:7(given)
Let y=3a & z= 7a
Putting this value in eq iii
z+ y=180°
7a+3a=180°
10a=180°
a= 180/10= 18°
z=7a= 7×18=126°
As we know x=z
∴x=z=126∘
Hence, the value of x= 126°
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Hope this will help you....