In the adjoining figure, AB $∥$ CD. Find the value of $x$ .

x = 40^{\circ}

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x = 30^{\circ}

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x = 50^{\circ}

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None of these

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Solution

The correct option is D $x = 40^{\circ}$
$G i v e n ∠ D C E = 100^{o} & ∠ A B E = 120^{o} L e t u s e x t e n d A B s u c h t h a t i t m e e t s C E a t F & e x t e n d s t i l l G . G i v e n A B ∥ C D, s o A G ∥ C D . L e t C E b e t h e t r a n s v e r s a l . T h e n ∠ D C E = ∠ G F E = 100^{o} [C o r r e s p o n d i n g a n g l e s] ∠ A B E + ∠ E B F = 180^{o} [S i n c e ∠ A B F i s a s t r a i g h t a n g l e] \Rightarrow ∠ E B F = 180 - 120 = 60^{o} ∠ G F E + ∠ E F B = 180^{o} [S i n c e ∠ B F G i s a s t r a i g h t a n g l e] \Rightarrow ∠ E F B = 180 - 100 = 80^{o} N o w i n △ B F E, ∠ E B F + ∠ E F B + ∠ F E B = 180^{o} \Rightarrow 60 + 80 + x^{o} = 180^{o} \Rightarrow x^{o} = 180 - 140 \Rightarrow x^{o} = 40^{o}$

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