In the figure measures of some angles are given. Which two lines are parallel and which two arc not ? Justify

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Solution

$F r o m t h e f i g u r e, 75^{o} + ∠ 1 = 180^{o} \Rightarrow ∠ 1 = 180 - 75 = 105^{o} [L i n e a r p a i r] ∠ 1 = ∠ 3 = 105^{o} [I n t e r i o r A l t e r n a t e A n g l e s] S o l i n e l i s p a r a l l e l t o l i n e m . ∠ 3 = ∠ 2 = 105^{o} [V e r t i c a l l y O p p o s i t e A n g l e s] I f l i n e m i s p a r a l l e l t o l i n e n t h e n ∠ 2 + ∠ 4 = 180^{o} [i n t e r i o r c o r r e s p o n d i n g a n g l e s] B u t h e r e ∠ 2 + ∠ 4 = 105^{o} + 65^{o} = 170^{0} s o ∠ 2 + ∠ 4 \neq 180^{o} S o l i n e m i s n o t p a r a l l e l t o l i n e n .$

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