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

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In the given figure, AB || CD, CD || EF 

and y : z = 3 : 7. 

Let y = 3a and z = 7a 

∠DHI = y (vertically opposite angles) 

∠DHI + ∠FIH = 180° 

(Interior angles on the same side of the transversal) 

⇒ y + z = 180° 

⇒ 3a + 7a = 180° 

⇒ 10a = 180° ⇒ a = 18° 

∴ y = 3 × 18° = 54° and z = 18° × 7 = 126° 

Also, x + y = 180° 

⇒ x + 54° = 180° 

∴ x = 180° – 54° = 126° 

Hence, x = 126° Ans.

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