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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Subjective Medium Published on 09th 09, 2020
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