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