Question

Two supplementary angles are such that the measure of one angle is 4/5 of the measure of the other angle. Find the measure of the measure

Answer 1

Given :

• Measure of one supplementary angle is 4/5 .

To Find :

• Measure of other supplementary angle .

Solution :

$\longmapsto\tt{Let\:one\:angle\:be=x}$

$\longmapsto\tt{Other\:angle=\dfrac{4x}{5}}$

As we know that the sum of supplementary angles is 180° . So ,

$\longmapsto\tt{\dfrac{4x}{5}+x=180}$

$\longmapsto\tt{\dfrac{5x+4x}{5}=180}$

$\longmapsto\tt{\dfrac{9x}{5}=180}$

$\longmapsto\tt{x=\dfrac{180\times{5}}{9}}$

$\longmapsto\tt\bf{x=100}$

VERIFICATION :

$\longmapsto\tt{\dfrac{4}{{\cancel{5}}}\times{{\cancel{100}}}+100=180}$

$\longmapsto\tt{4\times{20}+100=180}$

$\longmapsto\tt{80+100=180}$

$\longmapsto\tt\bf{180=180}$

HENCE VERIFIED

Answer 2

Answer:

Given :-

• Two supplementary angles are such that the measure of one angles is ⅘ of the measure of the other angle.

To Find :-

• What is the measure of the angle.

Solution :-

Let,

$\small\mapsto \bf One\: Angle_{(Supplementary\: Angle)} =\: a$

$\small\mapsto \bf Another\: Angle_{(Supplementary\: Angle)} =\: \dfrac{4a}{5}$

As we know that :

$\footnotesize\bigstar\: \: \sf\boxed{\bold{\pink{Sum\: Of\: The\: Measures\: Of\: Two\: Supplementary\: Angle =\: 180^{\circ}}}}\: \: \bigstar$

According to the question by using the formula we get,

$\implies \bf \bigg\{a\bigg\} + \bigg\{\dfrac{4a}{5}\bigg\} =\: 180^{\circ}$

$\implies \sf a + \dfrac{4a}{5} =\: 180^{\circ}$

$\implies \sf \dfrac{5a + 4a}{5} =\: 180^{\circ}$

By doing cross multiplication we get,

$\implies \sf 5a + 4a =\: 5(180^{\circ})$

$\implies \sf 5a + 4a =\: 5 \times 180^{\circ}$

$\implies \sf 9a =\: 900^{\circ}$

$\implies \sf a =\: \dfrac{\cancel{900^{\circ}}}{\cancel{9}}$

$\implies \sf a =\: \dfrac{100^{\circ}}{1}$

$\implies \sf\bold{\purple{a =\: 100^{\circ}}}$

Hence, the measure of the each supplementary angles are :

❒ One Angle Of Supplementary Angle :

$\small\longrightarrow \sf One\: Angle_{(Supplementary\: Angle)} =\: a$

$\small\longrightarrow \sf\bold{\red{One\: Angle_{(Supplementary\: Angle)} =\: 100^{\circ}}}$

❒ Another Angle Of Supplementary Angle :

$\small\longrightarrow \sf Another\: Angle_{(Supplementary\: Angle)} =\: \dfrac{4a}{5}$

$\small\longrightarrow \sf Another\: Angle_{(Supplementary\: Angle)} =\: \dfrac{4 \times 100^{\circ}}{5}$

$\small\longrightarrow \sf Another\: Angle_{(Supplementary\: Angle)} =\: \dfrac{\cancel{400^{\circ}}}{\cancel{5}}$

$\small\longrightarrow \sf\bold{\red{Another\: Angle_{(Supplementary\: Angle)} =\: 80^{\circ}}}$

${\footnotesize{\bold{\underline{\therefore\: The\: measure\: of\: supplementary\: angles\: are\: 80^{\circ}\: and\: 100^{\circ}\: respectively\: .}}}}$