Find the value of x in each of the following figures if $ι ∥ m$ .

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Solution

$I n f i g u r e 1,$

$∠ H G B = ∠ A G E$

$∠ H G B = 110^{o}$

$F r o m p a r a l l e l l i n e s L a n d M, w i t h t r a n s v e r s a l T$

$∠ H G B + ∠ G H D = 180^{o}$
$X = 180^{o} - 110^{o}$

$X = 70^{o}$

$I n f i g u r e 2,$

$F r o m p a r a l l e l l i n e s L a n d M, w i t h t r a n s v e r s a l A$

$∠ A I E = ∠ C J I$

$100^{o} = X$

${X = 100}^{o}$

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