Question

Lines m ‖ n and p ‖ q in the given figure, then find the value of a, b, c, d.​

Answer 1

$Given \: m \parallel n \:and \: p\parallel q$

$i) m \parallel n \:and \: Transversal \: 'p' .$

$a + 120 = 180\degree$

$\blue{( Sum \:of \: interior\: angles \: same }$

$\blue{ side\:of \: the \:transversal \:are }$

$\blue{ supplementary )}$

$\implies a = 180 - 120$

$\implies a = 60 \degree \: --(1)$

$ii) p \parallel q \:and \: Transversal \: 'm' .$

$a + c = 180\degree$

$\blue{( Sum \:of \: interior\: angles \: same }$

$\blue{ side\:of \: the \:transversal \:are }$

$\blue{ supplementary )}$

$\implies 60 + c = 180$

$\implies c = 180 - 60$

$\implies c = 120 \degree \: --(2)$

$iii) c = d \: \blue{( Vertically \: opposite \:angles ) }$

$\implies d = 120\degree \: --(3)$

$iv) b = d$

$\blue{ ( Corresponding \: angles )}$

$\implies b = 120\degree \: ---(4)$

Therefore.,

$a = 60 \degree, \: b = 120\degree,$

$c = 120\degree\:and \: d = 120\degree$

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Answer 2

Answer:

Hope it helps a lot ...

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