Question

Among two supplementary angles, the measure of the larger angle is 36 degree more than the measure of the smaller.Find their measure​

Answer 1

Answer:

72°

Step-by-step explanation:

let the measure of the smaller angle be x.

:. measure of the larger angle = x+36

=> x+x+36 = 180. [ as it is supplementary ]

=> 2x = 180-36

=> x = 144/2

=> x = 72

Therefore, the value of x is 72

smaller angle = 72°

larger angle = 72+36 = 108°

hope this helps you

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Answer 2

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

Among two supplementary angles, the measure of the larger angle is 36 degree more than the measure of the smaller.

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

$\sf \implies The \: measures \: of \: both \: the \: angles.$

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

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

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

$\sf \implies Larger \: angle \: be \: (x + 36^{\circ})$

$\sf We \: already \: know \: that,$

$\underline{ \boxed{ \sf Sum \: of \: two \: supplementary \: angles \: is \: 180^{\circ}}}$

$\sf \implies So, smaller \: angle + larger \: angle = 180^{\circ}$

$\sf \underline{According \: to \: question},$

$\sf \implies x + (x + 36) = 180^{\circ}$

$\sf \implies x + x + 36= 180^{\circ}$

$\sf \implies 2x + 36 = 180^{\circ}$

$\sf \implies 2x = 180 - 36$

$\sf \implies 2x = 144$

$\sf \implies x = \cancel{\dfrac{144}{2} }$

$\sf \implies x = 72$

$\bf \underline{ Therefore},$

$\sf \implies Smaller \: angle \: \bf(x) = 72^{\circ}$

$\sf \implies Larger \: angle \bf \: = (x + 36^{\circ}) = 72 + 36 = 108^{\circ}$

$\underline{ \boxed{ \bf \red{Hence, measures \: of \: both \: the \: angles = 72^{\circ} \: and \:108^{\circ} }}}$

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

$\underline{ \sf Sum \: of \: two \: supplementary \: angles = 180^{\circ}}$

$\sf \implies Larger \: angle = 108^{\circ}$

$\sf \implies Smaller \: angle = 72^{\circ}$

$\sf \implies108^{\circ} + 72^{\circ}= 180^{\circ}$

$\sf \implies 180^{\circ}= 180^{\circ}$

$\sf \implies LHS= RHS$

$\bf \underline{ Hence \: Verified \: !!}$