Question

prove that adjacent angles of a parallelogram are supplementary . with diagram

Answer 1

$\boxed{\boxed{\boxed{\bold{\blue{Solution : \longrightarrow}}}}}$

$\bold{Let \: \: ABCD \: \: be \: \: a \: \: || gm.}$

$\bold{\underline{To \: \: prove \: \: that}}$

$\bold{ ∠ A +∠ B = ∠ B + ∠ C = ∠ C +} \\ \bold{∠ D = ∠ D + ∠A = 180°}$

$\bold{\underline{Proof :}}$

$\bold{AD || BC \: \: and \: \: AB \: \: is \: \: the \: \: transversal.}$

$\bold{Therefore, \: \: ∠ A + ∠ B = 180° \: \: [Since \: \: }\\ \bold{sum \: \: of \: \: interior \: \: angles \: \: on \: \: the} \\ \bold{same \: \: side \: \: of \: \: the \: \: transversal \: \: is }\\ \bold{ 180°}]$

$\bold{Similarly,} \\ \\ \bold{ ∠ B + ∠ C = 180°} \\ \\ \bold{∠ C + ∠ D = 180 °}\\ \\ \bold{∠ D +∠ A = 180°}$

$\bold{Hence, \: \: sum \: \: of \: \: any \: \: two \: \: adjacent}$
$\bold{angles \: \: of \: \: ||gm \: \: are \: \: supplementary.}$

$\boxed{\boxed{\boxed{\bold{\green{Have \: \: a \: \: nice \: \: day.}}}}}$