Mathematics

Find the measure of an angle which is $${18}^{\circ}{2}^{\prime}{10}^{\prime\prime}$$ less than its complement.


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

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

$$\left({90}^{\circ}-{x}^{\circ}\right)-{x}^{\circ}={18}^{\circ}{2}^{\prime}{10}^{\prime\prime}$$

$$\Rightarrow 2{x}^{\circ}={90}^{\circ}-{18}^{\circ}{2}^{\prime}{10}^{\prime\prime}$$

$$\Rightarrow 2{x}^{\circ}={89}^{\circ}{59}^{\prime}{60}^{\prime\prime}-{18}^{\circ}{2}^{\prime}{10}^{\prime\prime}={71}^{\circ}{57}^{\prime}{50}^{\prime\prime}$$

$$\Rightarrow {x}^{\circ}=\dfrac{{71}^{\circ}{57}^{\prime}{50}^{\prime\prime}}{2}={35}^{\circ}{58}^{\prime}{55}^{\prime\prime}$$

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