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 any angle be $a^{\circ }$
Then, its complement will be $(90–a{)}^{\circ }$

According to the question,
$a^{\circ }=\frac{1}{2}\left(\text{complement of}{a}^{\circ }\right)+{30}^{\circ }$
$a^{\circ }=\frac{(90-a{)}^{\circ }}{2}+{30}^{\circ }$
$2a^{\circ }={90}^{\circ }-a^{\circ }+{60}^{\circ }$
$2a^{\circ }+a^{\circ }={150}^{\circ }$
$3a^{\circ }={150}^{\circ }$
$a^{\circ }={50}^{\circ }$

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