Question

An angel is ${30}^{\circ }$more than one-half of its complement . Find the angle in degree.

Answer 1

Let us assume that the angle is $x$

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

It is given that, angle is ${30}^{\circ }$ more than one half of its complement.

$\Rightarrow {30}^{\circ }+\frac{{90}^{\circ }-x}{2}=x$

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

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

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

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

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

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

$\Rightarrow {50}^{\circ }=x$

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