Question

one angle of parallelogram is 60degres. find its opposite angle and the adjacent angle​

Answer 1

$\sf\circ \: if \: \angle \: a = 60 \degree \\ \underbrace{\sf \circ \: \angle \: c = 60 \degree \:} \\ \leadsto \: \underline \bold{reason} - \sf{opposite \: angles \: are \: equal}$

$\blacksquare \sf \: now \: lets \: find \: out \: adjacent \: angles \: by \: the \: property \: which \: is \: mentioned \: below$

$\sf \dagger \: property \: of \: a \: parallelogram :$

$\bigstar \: \underline{\underline \bold \red{sum \: of \: all \: the \: \angle \: es \: of \: a \: parallelogram = 180 \degree}}$

$\sf \Rrightarrow \: 60 \degree + 60 \degree + x + x = 180 \degree \\ \Rrightarrow \: 120 \degree + 2x = 180 \degree \\ \Rrightarrow \: 2x = 60 \degree$

$\Rrightarrow \: x = \frac{60}{2} = 30 \\ \bold{\underline{ \red{\leadsto \: 30 \degree }}}$

$\blacktriangleright \: \bold{ \angle \: a = 60 \degree} \\ \bold{\angle \: b = 30 \degree }\\ \bold{\angle \: c = 60 \degree }$

$\bold{\angle \: d = 30 \: \degree}$

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Answer 2

Step-by-step explanation:

$\sf\circ \: if \: \angle \: a = 60 \degree \\ \underbrace{\sf \circ \: \angle \: c = 60 \degree \:} \\ \leadsto \: \underline \bold{reason} - \sf{opposite \: angles \: are \: equal}$

$\blacksquare \sf \: now \: lets \: find \: out \: adjacent \: angles \: by \: the \: property \: which \: is \: mentioned \: below$

$\sf \dagger \: property \: of \: a \: parallelogram :$

$\bigstar \: \underline{\underline \bold \red{sum \: of \: all \: the \: \angle \: es \: of \: a \: parallelogram = 180 \degree}}$

$\sf \Rrightarrow \: 60 \degree + 60 \degree + x + x = 180 \degree \\ \Rrightarrow \: 120 \degree + 2x = 180 \degree \\ \Rrightarrow \: 2x = 60 \degree$

$\Rrightarrow \: x = \frac{60}{2} = 30 \\ \bold{\underline{ \red{\leadsto \: 30 \degree }}}$

$\blacktriangleright \: \bold{ \angle \: a = 60 \degree} \\ \bold{\angle \: b = 30 \degree }\\ \bold{\angle \: c = 60 \degree }$

$\bold{\angle \: d = 30 \: \degree}$

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