Question

two supplementary angles differ by 34. find the angles

Answer 1

Answer:

Required Supplementary angles are ,

(107°,73°)

Explanation:

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Supplementary angles:

Sum of any two angles equal to 180° are called supplementary angles .

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Here,

Let x , (180-x) are two supplementary angles.

According to the problem given,

x -(180°-x) = 34°

=> x -180°+x = 34°

=> 2x = 34+180

=> 2x = 214

=> x = 214/2

=> x = 107°

Therefore,

Required angles are ,

x = 107°,

180-x = 180-107 = 73°

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Answer 2

The angles are $\bold{73^{\circ} and\ 107^{\circ}}$

Given:

The difference of two angles is 34  

To find:

The angles

Solution:

Supplementary angles are those angles whose sum are equivalent to $180^{\circ}$

Now the question says that the value of their difference is 34. Therefore, to find the angles let us form two equations:

Let us take one angle as A and the other one as B, now as A and B are supplementary angle so we have our first equation as (A + B = 180), whereas the second equation is (A – B = 34). So now equate the equations

$\begin{array}{l}{A+B=180^{\circ}} \\ {A-B=34^{\circ}}\end{array}$

Deducting the value of B, we get A as

$2 A=214^{\circ} ; A=107^{\circ}$

Now with A as $107^{\circ}-B=34^{\circ}$; $107^{\circ}-34^{\circ}=B ; B=73^{\circ}$

Therefore, the value of A and B is 107 and 73 respectively.