In the figure AB ll CD …

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In the figure AB ll CD find x

Posted by Sayyam Sharma 5 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Sia ? 5 years, 5 months ago

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

2Thank You

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