In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x.

1.	In the given figure, if AB \|\| CD, CD \|\| EF and y: z = 3: 7, find x.
Answer» It is given that AB \|\| CD and CD \|\| EF ∴ AB \|\| CD \|\| EF (Lines parallel to the same line are parallel to each other) It can be observed that x = z (Alternate interior angles) … (1) It is given that y: z = 3: 7 Let the common ratio between y and z be a. ∴ y = 3a and z = 7a Also, x + y = 180º (Co-interior angles on the same side of the transversal) z + y = 180º [Using equation (1)] 7a + 3a = 180º 10a = 180º a = 18º ∴ x = 7a = 7 × 18º = 126º

Answer»

It is given that AB || CD and CD || EF

∴ AB || CD || EF (Lines parallel to the same line are parallel to each other) It can be observed that

x = z (Alternate interior angles) … (1)

It is given that y: z = 3: 7

Let the common ratio between y and z be a.

∴ y = 3a and z = 7a

Also, x + y = 180º (Co-interior angles on the same side of the transversal)

z + y = 180º [Using equation (1)]

7a + 3a = 180º

10a = 180º

a = 18º

∴ x = 7a = 7 × 18º = 126º

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