Question

The larger of two supplementary angle exceeds the smaller by 18°. find them.
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Answer 1

a + b = 180

a = b + 18

a + 18 + b = 180

2b = 162

b = 81

a = 81 + 18

a = 99

Two supplementary angles are 99 and 81 .

Answer 2

$\bf \underline{ \underline{\maltese\:Given} }$

The larger of two supplementary angle exceeds the smaller by 18°

$\bf \underline{ \underline{\maltese\:To \: find } }$

$\sf \implies The \: numbers = \: ?$

$\bf \underline{ \underline{\maltese\:Solution } }$

$\sf Let \: us \: assume \: that,$

$\sf \implies Larger \: angle \: be \: x$

$\sf \implies Smaller \: angle \: be \: y$

$\sf According \: to \: question,$

$\sf \implies x - y = 18 \: \: \: \: \: \rm[Equation : 1]$

$\sf \implies x + y = 180\: \: \: \: \: \rm[Equation : 2]$

$\bf \underline{Now},$

$\sf By \: equation : 1$

$\sf \implies x - y = 18$

$\sf \implies x = 18 + y$

$\sf Putting \: x \: in \: equation : 2$

$\sf \implies x + y = 180$

$\sf \implies (18 + y) + y = 180$

$\sf \implies 18 + y + y = 180$

$\sf \implies 18 + 2y = 180$

$\sf \implies 2y = 180 - 18$

$\sf \implies 2y = 162$

$\sf \implies y = \cancel\dfrac{162}{2}$

$\bf \implies y = 81$

$\bf \underline{Now}, \sf substituting \: value \: of \: y \: in \: equation : 1$

$\sf \implies x - y = 18$

$\sf \implies x - 81 = 18$

$\sf \implies x = 18 + 81$

$\sf \implies x = 99$

$\sf \underline{So, value \: of \: x \: is \: 99 \: and \: y \: is \: 81}$

$\bf \underline{ Therefore},$

$\sf \implies Larger \: angle \: (x) = \bf 99^{\circ}$

$\sf \implies Smaller \: angle \:( y ) = \bf81^{\circ}$