Question

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

Answer 1

We know, two angles are said to be complementary, if the sum of their measures is ${90}^{\circ }.$

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

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

We can write, ${90}^{\circ }={89}^{\circ }{59}^{\prime }{60}^{\prime \prime }$.

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

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

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

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

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