In the given figure $A B ∥ C D$ . find the value of x and y.

x = 35^{\circ}, y = 65^{\circ}

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x = 95^{\circ}, y = 65^{\circ}

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x = 85^{\circ}, y = 65^{\circ}

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x = 25^{\circ}, y = 65^{\circ}

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Solution

The correct option is D $x = 85^{\circ}, y = 65^{\circ}$
$G i v e n A B ∥ C D & R Q i s t h e t r a n s v e r s a l t h e n ∠ Q H C = ∠ A F H = 115^{o} {C o r r e s p o n d i n g a n g l e s} N o w y + ∠ A F H = 180^{o} {L i n e a r p a i r} \Rightarrow y = 180^{o} - 115^{o} \Rightarrow y = 65^{o} N o w A B ∥ C D & P Q i s t h e t r a n s v e r s a l t h e n ∠ P B F = x {C o r r e s p o n d i n g a n g l e s} S o x = 85^{o}$

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