Mathematics

# Find the measure of an angle which is ${5}^{\circ}{10}^{\prime}{16}^{\prime\prime}$ more than its supplement.

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

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

${x}^{\circ}-\left({180}^{\circ}-{x}^{\circ}\right)={5}^{\circ}{10}^{\prime}{16}^{\prime\prime}$

$\Rightarrow 2{x}^{\circ}={180}^{\circ}+{5}^{\circ}{10}^{\prime}{16}^{\prime\prime}$

$\Rightarrow 2{x}^{\circ}={185}^{\circ}{10}^{\prime}{16}^{\prime\prime}$

$\Rightarrow {x}^{\circ}=\dfrac{{185}^{\circ}{10}^{\prime}{16}^{\prime\prime}}{2}={92}^{\circ}{35}^{\prime}{8}^{\prime\prime}$

The measure of the angle is ${35}^{\circ}{58}^{\prime}{55}^{\prime\prime}$

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Subjective Medium Published on 09th 09, 2020
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