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Quadrilaterals

In the follow...

Question

In the following figure, $A B C D$ is a parallelogram. Find the value of $x$

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Solution

The correct option is B $12$
$G i v e n t h a t A B C D i s a p a r a l l e l o g r a m . W e k n o w t h a t i n a p a r a l l e l o g r a m o p p o s i t e a n g l e s a r e e q u a l . S o f r o m t h e g i v e n f i g u r e, ∠ B = ∠ D \Rightarrow 6 x + 3 y - 8 = 7 y \Rightarrow 6 x - 4 y = 8 \Rightarrow x = \frac{8 + 4 y}{6} - - - - (1) A l s o w e k n o w t h a t a d j a c e n t a n g l e s i n a p a r a l l e l o g r a m a r e s u p p l e m e n t a r y . S o ∠ A + ∠ D = 180^{o} \Rightarrow 4 x + 20 + 6 x + 3 y - 8 = 180^{o} \Rightarrow 10 x + 3 y = 168 - - - - (2) U s i n g 1 i n 2, 10 (\frac{8 + 4 y}{6}) + 3 y = 168 \Rightarrow 80 + 40 y + 18 y = 168 \times 6 \Rightarrow 58 y = 1008 - 80 \Rightarrow 58 y = 928 \Rightarrow y = \frac{928}{58} \Rightarrow y = 16^{o} U s i n g y = 16 i n 1, x = \frac{8 + 4 \times 16}{6} \Rightarrow x = \frac{8 + 64}{6} \Rightarrow x = \frac{72}{6} \Rightarrow x = 12^{o} S o x = 12^{o} & y = 16^{o}$

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