Question

If an angle is ${30}^{\circ }$ more than one half of its complement, find the measure of the angle.

Answer 1

Let the measure of the required angle = x
$\therefore$ Its complement = ${90}^{\circ }-x$
$\therefore x=\frac{1}{2}({90}^{\circ }-x)+{30}^{\circ }$
$2x={90}^{\circ }-x+{60}^{\circ }$
$\Rightarrow 2x+x={90}^{\circ }+{60}^{\circ }\Rightarrow 3x={150}^{\circ }$
$\therefore x=\frac{{150}^{\circ }}{3}={50}^{\circ }$ $\therefore$ Required angle = ${50}^{\circ }$