Question

The Opposite angles of a parallelogram are 2x+10degree and 3x-15 degree find the measurement

Answer 1

$\huge\sf{answer - }$

$\underline\bold{\dagger \: let \: angles\: of \: the \: parallelogram \: be - } \\ \sf\star \: \angle \: a \\ \sf\star \: \angle \: b \\ \sf\star \:\angle \: c \\ \sf\star \:\angle \: d$

$\underline\bold{\maltese \: according \: to \: the \: question - } \\ \sf \bigstar \: opposite \: angles \: are \: equal.$

$\bold{as \: angles \: are \: opposite} \\ \sf\therefore \: \angle \: a = 2x + 10 \degree \\ \bold{and} \\ \sf\angle \: c = 3x - 15 \degree$

$\underline \color{red}\bold{ \leadsto \: as \: we \: know \: opposite \: angles \: of \: a \: parallelogram \: are \: equal }$

$\bold{\hookrightarrow \: 2x + 10\degree = 3x - 15 \degree} \\ \bold{\hookrightarrow \: x = 25}$

$\underline\green{\maltese \: by \: putting \: the \: value \: of \: x \: we \: get - }$

$\hookrightarrow\bold{\angle \: a = 2 \times 25 + 10} \\ \hookrightarrow\bold{\angle \: a = 50 + 10 = 60\degree} \\ \sf{\angle \: a =} \fbox{60}$

$\bold{\underline\color{red}\leadsto \: also \: we \: know \: that \: sum \: of \: two \: adjacent \: angles \: of \: a \: parallelogram \: = \: 180\degree}$

$\bold{\hookrightarrow \: \angle \: a + \angle \: b = 180 \degree}$

$\bold{\hookrightarrow \: 60 + \angle \: b = 180\degree}$

$\hookrightarrow \bold{ \angle \: b = 180 \degree - 60 \degree} \\ \hookrightarrow\sf{\angle \: b =} \fbox{120}$

$\sf \underline\color{blue}\maltese \: and \: as \: we \: know \: opposite \: angles \: are \: equal \:$

$\blacktriangleright \bold{\angle \: a = \angle \: c = 60 \degree} \\ \blacktriangleright \bold{\angle \: b = \angle \: d = 120 \degree}$

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$\huge\sf\pink{verification - }$

$\bold {\hookrightarrow \: \angle \: a + \angle \: b + \angle \: c + \angle \: d = 360 \degree}$

$\bold{\hookrightarrow \: (60 + 120 + 60 + 120)\degree = 360 \degree} \\ \: \sf \underline{\hookrightarrow \: 360 \degree = 360 \degree} \red\checkmark$

$\color{gold}\star\fbox{\underline{hence \: verified}}$

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