Mathematics

# Find the measure of an angle if its supplement-three times complement $={20}^{\circ}{30}^{\prime}{40}^{\prime\prime}$

##### SOLUTION
Let the measure of an angle be ${x}^{\circ}$

$\therefore$ measure of its supplement$={180}^{\circ}-{x}^{\circ}$

The measure of its complement$={90}^{\circ}-{x}^{\circ}$

$\Rightarrow \left({180}^{\circ}-{x}^{\circ}\right)-3\left({90}^{\circ}-{x}^{\circ}\right)={20}^{\circ}{30}^{\prime}{40}^{\prime\prime}$

$\Rightarrow \left({180}^{\circ}-{x}^{\circ}\right)-{270}^{\circ}+3{x}^{\circ}={20}^{\circ}{30}^{\prime}{40}^{\prime\prime}$

$\Rightarrow 2{x}^{\circ}={20}^{\circ}{30}^{\prime}{40}^{\prime\prime}+{90}^{\circ}$

$\Rightarrow 2{x}^{\circ}={110}^{\circ}{30}^{\prime}{40}^{\prime\prime}$

$\Rightarrow {x}^{\circ}=\dfrac{{110}^{\circ}{30}^{\prime}{40}^{\prime\prime}}{2}$

$\Rightarrow {x}^{\circ}={55}^{\circ}{15}^{\prime}{20}^{\prime\prime}$

The measure of the angle is ${55}^{\circ}{15}^{\prime}{20}^{\prime\prime}$

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Subjective Medium Published on 09th 09, 2020
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