Question

The ratio of two supplementary angles is 4:1. Find the measures of both angles.


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Answer 1

Given :

• Ratio of two supplementary angles is 4 : 1

To Find :

• The measures of both angles

Solution :

• Let the ratio constant be 'x'

Then the both angles are 4x , 1x

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• Using the relation ,

$\\ \star \large\boxed{\sf{ \purple{sum \: of \: two \: supplementary \: angles = 180 {}^{ \circ} }}}$

$\\ : \implies \sf \: 4x + 1x = 180 {}^{ \circ} \\ \\ \\ : \implies \sf \: 5x = {180}^{ \circ} \\ \\ \\ : \implies \sf \: x = \frac{ {180}^{ \circ} }{5} \\ \\ \\ : \implies{\boxed{\sf{\underline{x = 36 {}^{ \circ} }}}}$

Then the both angles are ,

$\\ \sf \: 4x = 4(36) = 144 {}^{\circ} \\ \\ \sf \: 1x = 1(36) = {36}^{ \circ}$

Hence , The Measures of both angles are 144° and 36° .

Answer 2

Answer:

Let the ratio of two supplementary angles be 4x and x .

4x + x = 180°

5x = 180°

x = 180°/5

x = 36°

therefore 4x = 4×36°

= 144°

Therefore 36° and 144° are the two supplementary angles.

Explanation:

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