In the figure AB ll CD …

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In the figure AB ll CD find x

Posted by Sayyam Sharma 5 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 10 months ago

Construction : Draw EF || AB || CD
As AB || EF and transversal AE cuts them
$\therefore$ $\angle$ BAE + $\angle$ FEA = 180^o . . . . . [Interior angles on same side of transversal are supplementary]
$\therefore$ 108^o + $\angle$ FEA = 180^o
$\therefore$ $\angle$ FEA = 180^o – 108^o = 72^o
As EF || CD and a transversal EC intersects them
$\angle$ FEC + $\angle$ ECD = 180^o . . . . . [Interior angles on same side of transversal are supplementary]
$\therefore$ $\angle$ FEC + 112^o = 180^o
$\therefore$ $\angle$ FEC = 180^o – 112^o = 68^o
$\therefore$ x^o = $\angle$ AEC = $\angle$ FEA + $\angle$ FEC = 72^o + 68^o = 140^o
$\therefore$ x = 140^o

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