Question

the difference between two supplementary angles is 54 degrees find the two angles

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Answer 1

Given :

• Difference between two angles are 54°

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To find :

• Measure of two angles whose difference gives us 54°

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Before jumping directly into the question lets know what is meant by supplementary angles.

Simply, supplementary angles are those which when added gives us 180° .

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Assumption :

• Let the two supplementary angles be x and y.

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Solution :

We know that :

$\small\fbox\purple{Sum~of~two~Supplementary~angles~=~180~degree}$

$\sf\:x+y=180^{°}$ -- $\small\fbox{1}$

‎$\sf\:x-y=54^{°}$ -- ( from given ) -- $\small\fbox{2}$

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Adding 1 and 2 -

$\sf\:(x+y)+(x-y)=180^{°}+54^{°}$

$\sf\implies\:x+y+x-y=234^{°}$

Arranging the terms

$\sf\implies\:x+x+y-y=234^{°}$

Terms with opposite signs gets cancelled

$\sf\implies\:x+x+\cancel{y}-\cancel{y}=234^{°}$

$\sf\implies\:x+x=234^{°}$

Adding the like terms

$\sf\implies\:2x=234^{°}$

Transposing 2 in RHS it goes to the denominator

$\sf\implies\:x=\frac{234^{°}}{2}$

Reducing the fraction

$\sf\implies\:x=\cancel{\frac{234^{°}}{2}}$

$\small{\underline{\boxed{\mathrm{\implies\:x=117^{°}}}}}$

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Plugging the value of x in 1 -

$\sf\:x+y=180^{°}$

$\sf\implies\:117^{°}+y=180^{°}$

Transposing +117 to RHS it becomes -117

$\sf\implies\:y=180^{°}-117^{°}$

$\small{\underline{\boxed{\mathrm{\implies\:y=63^{°}}}}}$

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Henceforth the two angles are :

• x = $\large{\mathfrak\red{117~degree}}$ $\tt\color{black}{⋆}$

• y = $\large{\mathfrak\red{63~degree}}$ $\tt\color{black}{⋆}$

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Verification :

Let's add the two angles we got , in order to check whether it follows the criteria for supplementary angles.

Criteria : $\sf\:x+y=180^{°}$

Plugging the value of angles we got

‎$\sf\leadsto\:117^{°}+63^{°}=180^{°}$

‎$\sf\leadsto\:180^{°}=180^{°}$

‎$\bf\leadsto\:LHS=RHS$

Hence Verified !~

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Answer 2

Answer:

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