Question

Find the measure of an angle if its supplement-three times complement $={20}^{\circ }{30}^{\prime }{40}^{\prime \prime }$

Answer 1

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

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

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

$\Rightarrow ({180}^{\circ }-x^{\circ })-3({90}^{\circ }-x^{\circ })={20}^{\circ }{30}^{\prime }{40}^{\prime \prime }$

$\Rightarrow ({180}^{\circ }-x^{\circ })-{270}^{\circ }+3x^{\circ }={20}^{\circ }{30}^{\prime }{40}^{\prime \prime }$

$\Rightarrow 2x^{\circ }={20}^{\circ }{30}^{\prime }{40}^{\prime \prime }+{90}^{\circ }$

$\Rightarrow 2x^{\circ }={110}^{\circ }{30}^{\prime }{40}^{\prime \prime }$

$\Rightarrow x^{\circ }=\frac{{110}^{\circ }{30}^{\prime }{40}^{\prime \prime }}{2}$

$\Rightarrow x^{\circ }={55}^{\circ }{15}^{\prime }{20}^{\prime \prime }$

The measure of the angle is ${55}^{\circ }{15}^{\prime }{20}^{\prime \prime }$