Question

The opposite angle of a quadrilateral is supplementary to each other. If the difference between the pairs of opposite angles is 40° and 20°, Find the measure of the angles of the quadrilateral ​

Answer 1

$\large{\red{ \bf{ \underline {\underline{Answer}}}}} \\ \\ \purple{ \sf{\mapsto The \: angle \: are \: 110 \degree, \: 100 \degree, 80 \degree, \: 70 \degree}} \\ \\ \mathrm{\green{ \underline{Given}}} \\ \\ \sf{\rightsquigarrow The \: two \: opposite \: angle \: of \: quadrilaterals} \\ \sf {are \: supplymentary \: to \: each \: other , \: } \\ \sf{ difference \: between \: the \: pairs \: of \: opposite} \\ \sf{angle \: is \: 40 \degree and \: 20 \degree}\\ \\ \rm{ \blue{ \underline{To \: Find}}} \\ \\ \sf{\rightsquigarrow Measure \: of \: the \: angle \: of \: the \: quadrilateral}$

• According to given question

$\sf{Let \: the \: angle \: be \: abcd \: respectively} \\ \\ \sf{A + D = 180 \degree - - - - (1)} \: given \\ \sf{B + C = 180 \degree} - - - - (2)\: given \\ \\ \sf{A - D = 40 \degree - - - - (3)}\: given \\ \sf{B - C = 20 \degree - - - - (4)}\: given \\ \\ \sf{ \therefore \: \: Adding \: equation \: (1) + equation \: (3)} \\ \\ \sf{ \implies (A + D = 180 \degree) + (A - D = 40 \degree)} \\ \\ \sf{ \implies 2A = 220 \degree} \\ \\ \sf{ \implies A = \frac{ \cancel{220 }}{ \cancel{2} }} \\ \\ \sf \purple{ \implies \purple {\underline{ \boxed {\sf{A = 110 \degree}}}}} \\ \\ \sf{Substituting \: value \: of \: A \: in \: equation \: (3)} \\ \\ \sf{ \implies 110 \degree - D = 40 \degree} \\ \\ \sf{ \implies D = 110 \degree - 40 \degree} \\ \\ \sf \purple{ \implies \purple {\underline{ \boxed {\sf{D = 70 \degree}}}}}$

$\sf{ Now, \: equation \:(2) + equation \: (4)} \\ \\ \sf{ \implies (B + C = 180 \degree) + (B - C = 20 \degree)} \\ \\ \sf{ \implies 2B = 200 \degree} \\ \\ \sf{ \implies B = \frac{ \cancel{200}}{ \cancel{2} }} \\ \\ \sf{ \purple{ \implies }} \purple{ \underline{ \boxed{ \sf{B = 100 \degree}}}} \\ \\ \sf{ \therefore \: \: Subtituting\:Value \: of \: B \: in \: equation \: (4)} \\ \\ \sf{ \implies 100 \degree - C = 20 \degree} \\ \\ \sf{ \implies C = 100 \degree - 20 \degree } \\ \\ \sf{ \purple{ \implies }} \purple{ \underline{ \boxed{ \sf{C = 80 \degree}}}} \\ \\ \sf \purple{ \therefore \: \:The \: angle \: are \: 110 \degree, \: 100 \degree, \: 80 \degree, \:70 \degree}$

$\sf{\purple{\dag\:\angle A=110\degree}}$

$\sf{\purple{\dag\:\angle B=100\degree}}$

$\sf{\purple{\dag\:\angle C=80\degree}}$

$\sf{\purple{\dag\:\angle D=70\degree}}$

Answer 2

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• Opposite angles of a quadrilateral is supplementary.
• Difference between pairs of opposite angles is 40° & 20°

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$\red{\underline \bold{To \: Find:}}$

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• Measure of angles of the quadrilateral

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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Let one one pair of opposite angle be x & y

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So,

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⇛ x + y = 180° --------(1)

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⇛ x - y = 40° -----------(2)

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$\underline{\bold{\texttt{Solving (1) \& (2) we get,}}}$

$\:\:$

⇛ 2x = 220

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⇛ x = 110°

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Hence,

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⇛ y = 70°

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Let other pair of opposite angles be a & b

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So,

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⇛ a + b = 180° ----------(3)

$\:\:$

⇛ a - b = 20° -----------(4)

$\:\:$

$\underline{\bold{\texttt{Solving (3) \& (4) we get,}}}$

$\:\:$

⇛ 2a = 200

$\:\:$

⇛ a = 100°

$\:\:$

Hence,

$\:\:$

⇛ b = 80°

$\:\:$

$\underline{\bold{\texttt{Hence angles are :}}}$

• 110°
• 70°
• 100°
• 80°

$\rule{200}5$