If an angle is $30^o$ more than one half of its complement, find the measure of the angle.

Given:

An angle is $30^o$ more than one half of its complement.

To do:

We have to find the measure of the angle.

Solution:

An angle is said to be the complement of another angle if the sum of both the angles is $90^o$.

If $x$ is an angle, then its complement is $90^o - x$.

Let the required angle be $x$.

This implies,

Complement of angle $x=90^o-x$

According to the question,

$x=\frac{1}{2}(90^o-x)+30^o$

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

$2x=150^o-x$

$3x=150^o$

$x=\frac{150^o}{3}$

$x=50^o$

Hence, the required angle is $50^o$.