Question

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

Answer 1

Let us assume that the angle is $x$.

Then, its complement will be ${90}^{\circ }-x$.

$30$ degree more than one half of its complement is ${30}^{\circ }+\frac{({90}^{\circ }-x)}{2}$
According to the sum, $x={30}^{\circ }+\frac{({90}^{\circ }-x)}{2}$

$\Rightarrow x=\frac{{60}^{\circ }+{90}^{\circ }-x}{2}$

$\Rightarrow x=\frac{{150}^{\circ }-x}{2}$

$\Rightarrow 2x={150}^{\circ }-x$

$\Rightarrow 3x={150}^{\circ }$

$\Rightarrow x=\frac{{150}^{\circ }}{3}$

$\therefore x={50}^{\circ }$
Hence, the required angle is ${50}^{\circ }$.