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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