The opposite angle of a quadrilateral is supplementary to each other.

1.	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» $\large{\red{ \bf{ \underline {\underline{Answer}}}}} \\ \\ \purple{ \sf{\mapsto The \: angle \: are \: 110 \degree, \: 100 \degree, 80 \degree, \: 70 \degree}} \\ \\ \mathrm{\green{ \underline{<klux>GIVEN</klux>}}} \\ \\ \sf{\rightsquigarrow The \: two \: opposite \: angle \: of \: quadrilaterals} \\ \sf {are \: supplymentary \: to \: each \: other , \: } \\ \sf{ difference \: between \: the \: pairs \: of \: opposite} \\ \sf{angle \: is \: 40 \degree and \: 20 \degree}\\ \\ \rm{ \blue{ \underline{To \: Find}}} \\ \\ \sf{\rightsquigarrow Measure \: of \: the \: angle \: of \: the \: quadrilateral}$ ACCORDING to given QUESTION $\sf{Let \: the \: angle \: be \: abcd \: respectively} \\ \\ \sf{A + D = 180 \degree - - - - (1)} \: given \\ \sf{B + C = 180 \degree} - - - - (2)\: given \\ \\ \sf{A - D = 40 \degree - - - - (3)}\: given \\ \sf{B - C = 20 \degree - - - - (4)}\: given \\ \\ \sf{ \therefore \: \: Adding \: equation \: (1) + equation \: (3)} \\ \\ \sf{ \implies (A + D = 180 \degree) + (A - D = 40 \degree)} \\ \\ \sf{ \implies 2A = 220 \degree} \\ \\ \sf{ \implies A = \frac{ \cancel{220 }}{ \cancel{2} }} \\ \\ \sf \purple{ \implies \purple {\underline{ \boxed {\sf{A = 110 \degree}}}}} \\ \\ \sf{Substituting \: value \: of \: A \: in \: equation \: (3)} \\ \\ \sf{ \implies 110 \degree - D = 40 \degree} \\ \\ \sf{ \implies D = 110 \degree - 40 \degree} \\ \\ \sf \purple{ \implies \purple {\underline{ \boxed {\sf{D = 70 \degree}}}}}$ $\sf{ Now, \: equation \:(2) + equation \: (4)} \\ \\ \sf{ \implies (B + C = 180 \degree) + (B - C = 20 \degree)} \\ \\ \sf{ \implies 2B = 200 \degree} \\ \\ \sf{ \implies B = \frac{ \cancel{200}}{ \cancel{2} }} \\ \\ \sf{ \purple{ \implies }} \purple{ \underline{ \boxed{ \sf{B = 100 \degree}}}} \\ \\ \sf{ \therefore \: \: Subtituting\:Value \: of \: B \: in \: equation \: (4)} \\ \\ \sf{ \implies 100 \degree - C = 20 \degree} \\ \\ \sf{ \implies C = 100 \degree - 20 \degree } \\ \\ \sf{ \purple{ \implies }} \purple{ \underline{ \boxed{ \sf{C = 80 \degree}}}} \\ \\ \sf \purple{ \therefore \: \:The \: angle \: are \: 110 \degree, \: 100 \degree, \: 80 \degree, \:70 \degree}$ $\sf{\purple{\dag\:\angle A=110\degree}}$ $\sf{\purple{\dag\:\angle B=100\degree}}$ $\sf{\purple{\dag\:\angle C=80\degree}}$ $\sf{\purple{\dag\:\angle D=70\degree}}$

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»

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

ACCORDING to given QUESTION

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

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