Question

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

Answer 1

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

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

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

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

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

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

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